Based on the meanings explained by the Salaf, and the Ahlus Sunnah (Ash'ari & Maturidi) scholars.
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وَإِذْ قَالَ رَبُّكَ لِلْمَلَائِكَةِ إِنِّي جَاعِلٌ فِي الْأَرْضِ خَلِيفَةً ۖ قَالُوا أَتَجْعَلُ فِيهَا مَن يُفْسِدُ فِيهَا وَيَسْفِكُ الدِّمَاءَ وَنَحْنُ نُسَبِّحُ بِحَمْدِكَ وَنُقَدِّسُ لَكَ ۖ قَالَ إِنِّي أَعْلَمُ مَا لَا تَعْلَمُونَ |30
وَعَلَّمَ آدَمَ الْأَسْمَاءَ كُلَّهَا ثُمَّ عَرَضَهُمْ عَلَى الْمَلَائِكَةِ فَقَالَ أَنبِئُونِي بِأَسْمَاءِ هَٰؤُلَاءِ إِن كُنتُمْ صَادِقِينَ |31
قَالُوا سُبْحَانَكَ لَا عِلْمَ لَنَا إِلَّا مَا عَلَّمْتَنَا ۖ إِنَّكَ أَنتَ الْعَلِيمُ الْحَكِيمُ |32
قَالَ يَا آدَمُ أَنبِئْهُم بِأَسْمَائِهِمْ ۖ فَلَمَّا أَنبَأَهُم بِأَسْمَائِهِمْ قَالَ أَلَمْ أَقُل لَّكُمْ إِنِّي أَعْلَمُ غَيْبَ السَّمَاوَاتِ وَالْأَرْضِ وَأَعْلَمُ مَا تُبْدُونَ وَمَا كُنتُمْ تَكْتُمُونَ |33
وَإِذْ قُلْنَا لِلْمَلَائِكَةِ اسْجُدُوا لِآدَمَ فَسَجَدُوا إِلَّا إِبْلِيسَ أَبَىٰ وَاسْتَكْبَرَ وَكَانَ مِنَ الْكَافِرِينَ |34
وَقُلْنَا يَا آدَمُ اسْكُنْ أَنتَ وَزَوْجُكَ الْجَنَّةَ وَكُلَا مِنْهَا رَغَدًا حَيْثُ شِئْتُمَا وَلَا تَقْرَبَا هَٰذِهِ الشَّجَرَةَ فَتَكُونَا مِنَ الظَّالِمِينَ |35
فَأَزَلَّهُمَا الشَّيْطَانُ عَنْهَا فَأَخْرَجَهُمَا مِمَّا كَانَا فِيهِ ۖ وَقُلْنَا اهْبِطُوا بَعْضُكُمْ لِبَعْضٍ عَدُوٌّ ۖ وَلَكُمْ فِي الْأَرْضِ مُسْتَقَرٌّ وَمَتَاعٌ إِلَىٰ حِينٍ |36
فَتَلَقَّىٰ آدَمُ مِن رَّبِّهِ كَلِمَاتٍ فَتَابَ عَلَيْهِ ۚ إِنَّهُ هُوَ التَّوَّابُ الرَّحِيمُ |37
قُلْنَا اهْبِطُوا مِنْهَا جَمِيعًا ۖ فَإِمَّا يَأْتِيَنَّكُم مِّنِّي هُدًى فَمَن تَبِعَ هُدَايَ فَلَا خَوْفٌ عَلَيْهِمْ وَلَا هُمْ يَحْزَنُونَ |38
وَالَّذِينَ كَفَرُوا وَكَذَّبُوا بِآيَاتِنَا أُولَٰئِكَ أَصْحَابُ النَّارِ ۖ هُمْ فِيهَا خَالِدُونَ |39
30. And remember when your God decreed to the angels, ‘I am going to appoint My vice-regent on earth’ ; they said, ‘Will You appoint such a one that he shall spread mischief in it and spill blood  and we reverently speak Your Glorification and Your Deification?’; He said, ‘I Know that which you do not know’ .
31. And [Allah Ta’ala] taught Adam the names of all things , then He placed all things in front of the angels and Said, ‘if you are truthful, tell their names.’ 
32. They said, ‘Glorified are You! we have no knowledge except that which You taught us; indeed You Alone are The One with knowledge and wisdom.’ 
33. He Said, ‘O Adam, tell them the names [of all things]’; when Adam told the names [of all things] , He said, ‘Did I not tell you that I Know all the hidden matters of the heavens and the earth, and I Know that which you manifest and that which you hide.’ 
34. And remember when We Commanded the angels to prostrate to Adam, and they all prostrated, except ibliis; he denied, and he was arrogant and he became a kafir. 
35. And We Decreed, ‘O Adam! you and your wife dwell in this jannah and eat from it without any hindrance whatever you wish, but do not approach this tree , or else you shall be from the transgressors.’ 
36. Then satan strayed them [from jannah] and separated them from where they stayed ; and We Decreed ‘descend down  one amongst you the enemy of the other, and for a certain time you have to stay on earth and bear it.’ 
37. Then Adam learnt some words from His God, and [He, Allah] forgave him , indeed He Alone is the Most Forgiving Most Merciful.
38. We Decreed, ‘all of you descend down [from jannah], then if any guidance comes to you from Me, then the one who followed My guidance, on them is neither fear nor grief.’ 
39. And those who commit kufr and belie Our signs, they are the people of hellfire, they shall abide therein unceasingly.
 – The khaliifah (caliph/vice-regent) is the representative of the one who appoints him, in matters of establishment of commandments, and other stipulations. Here, by khaliifah, our master Adam, ‘alaihis salam, is implicated, even though of course all other prophets are also Allah Ta’ala’s vice-regents. He stated in regards to our master Dawuud, ‘alaihis salam, (يَا دَاوُودُ إِنَّا جَعَلْنَاكَ خَلِيفَةً فِي الْأَرْضِ) (O Dawood, indeed We have appointed you khaliifah on earth… 38:26). The angels have been given the news of the khilaafah (caliphate/vice-regency) of Adam so that they enquire the wisdom behind making him a khaliifah and learn and they loftiness and magnificence of the khaliifah become manifest to them, that he [Adam] had been bestowed the title of ‘khaliifah’ before his creation itself, and dwellers of the heavens were given the glad tidings of his [Adam’s] creation.
Mas-ala (Case): In it, there is a lesson for the slaves that they should consult each other before a matter and Allah Ta’ala is Exalted from it that He should consult anyone. [Translator’s Note: The consultation is only between believers, as stated elsewhere in this exegesis. Muslims should not consult kuffaar for their matters.]
 – The aim of the angels’ questioning was not objection or jeering at our master Adam, but rather to learn the hikmah (wisdom) behind this khilaafah. And attributing humans to mischief, this knowledge is either granted to them from Allah’s Court, or obtained by them from the Lawh Al-Mahfouzdh (The Divinely Preserved Tablet), or they had themselves drawn an analogy observing the jinns [who also cause a lot of mischief].
 – It means to imply, ‘My wisdoms are not manifest to you and the thing is that humans will also incorporate ambiyaa (prophets), as well as awliyaa (saints), and also ‘ulamaa (scholars) and they shall be collectives of virtues of both scholarship (‘ilm) and [good] action (‘amal, ‘amal means action alone without implications of good or bad).
 – Allah Ta’ala showed our master Adam, ‘alaihis salam, all things and all their denominations and bestowed the knowledge of their names, attributes, actions, specialities, knowledge of their foundations and compositions – all of it, by way of ilhaam (pure inspiration from Him).
 – It means to say that ‘if you are truthful in your estimation that I shall not create any creation more knowledgeable than you, and only you [angels] are worthy of khilaafah, then tell the names of all these things!’ because the job of the khaliifah is dispersing and planning and justice and equality and this is not possible without the khaliifah having the knowledge of all those things over which he is appointed and on which he has to issue judgments.
Mas-ala (Case): Allah Ta’ala made manifest that the reason our master Adam, ‘alaihis salam, is superior to angels, is knowledge, and from this it is established that knowledge of names [i.e., of matters that pertain to oneself and what makes one worthy or not, similar to what is stated in this discussion on our master Adam’s khilaafah] is superior to the worships in solitudes and loneliness.
Mas-ala (Case): This ayah also establishes that the ambiyaa (prophets), ‘alaihimus salam, are exalted above angels.
 – In this, there is an admission of the humility and self-demerit by the angels and a manifestation of the matter that their question was for inquiring and NOT for objecting, and now they know the virtues of man, and the wisdom behind his creation, that they did not know before.
 – It means that Adam, ‘alaihis salam, stated the name of everything, and its birth and the wisdom behind it.
 – The matter that the angels made manifest was that mankind would spread mischief and spill blood, and the matter that they hid was that they [as they knew] are the ones worthy of khilaafah, and that Allah Ta’ala will not create any creation superior and more knowledgeable than them.
Mas-ala (Case): This verse proves mankind’s honor and the virtues of knowledge, and also that it is obviously valid to attribute Allah with knowledge, even though He can’t be called mu’allim (teacher) because a mu’allim is someone who teaches as a means of earning livelihood.
Mas-ala (Case): It also establishes that all languages [ever known to man] all dialects are from Allah.
Mas-ala (Case): It also establishes that the knowledge and loftiness of angels rise [that is, they’re not static].
 – Allah Ta’ala made our master Adam, ‘alaihis salam, as a manifestation of all that exists and a collective of the material and spiritual worlds, and rendered him as a means of obtaining loftiness for the angels. Therefore, they were commanded to prostrate (sajdah) to him because it contains thankfulness, an acknowledgement of the virtues of our master Adam, ‘alaihis salam, and a redress for their saying. Some mufassiriin (exegetes) state that Alla Ta’ala commanded the angels to prostrate to our master Adam, ‘alaihis salam, even before creating him; their evidence is this (فَإِذَا سَوَّيْتُهُ وَنَفَخْتُ فِيهِ مِن رُّوحِي فَقَعُوا لَهُ سَاجِدِينَ) (Then when I perfect him [i.e., his creation is complete] and bestow onto him a soul from My granting [i.e., grant him life], then you fall in prostration to him. 15:29 and 38:72) [Baidzaawiy]
The command to prostrate (perform sajdah) was given to the entirety of angels. This is the soundest opinion. [Khazen]
Mas-ala (Case): Sajdah (prostration) is of two types; 1) that of worship (‘ebaadah), which is done with the intention of complete and utter submission 2) that of greeting (tahiyyah), which is done with the intention of just praising the one being prostrated and NOT worship.
Mas-ala (Case): The sajdah of ‘ebaadah is reserved ONLY for Allah Ta’ala and can’t be performed for anyone else, and neither has it EVER been approved of in ANY shari’ah [given to any previous prophet]. Those exegetes who consider this prostration of the angels as a prostration of worship – they say that the sajdah was FOR ALLAH Ta’ala but our master Adam, ‘alaihis salam, was made the qiblah (the objectified direction to prostrate in, like our Qiblah is in Makkah) for this sajdah, THEREFORE he [Adam ‘alaihis salam] was the one in whose direction prostration was performed BUT NOT the one who was being prostrated. But this saying is dza’iif (weak) because the aim of this sajdah was to make manifest the honor and virtue of our master Adam, ‘alaihis salam, and it is not necessary that the one in whose direction prostration is performed be superior to the one prostrating, just as the Qiblah [in Makkah] is the direction in which our Master Rasulullah ﷺ prostrated, despite the fact that indeed our Master Rasulullah is abundantly more superior to it. The other saying is that here, the sajdah was not of worship, but rather greeting (tahiyyah) and was specially for our master Adam, ‘alaihis salam, and involved placing the forehead on the ground, rather than merely bowing. This saying is the soundest and the majority [of exegetes and scholars] are on this. [Madaarik]
Mas-ala (Case): The sajdah of tahiyyah (greetings) was allowed in former shari’ahs [given to previous prophets]. It has been abrogated in our shari’ah and it is NOT allowed for ANYONE now, because when our master Salman, radzi Allahu ‘anhu, intended to prostrate to our Master Rasulullah ﷺ, our Master commanded that the creation should not prostrate to anyone other than Allah. [Madaarik]
From the angels, the first one to prostrate was our master Jibriil, then our master Mikaaiil, the our master Israafiil, then our master ‘Azraaiil, the the other exalted angels. This sajdah was done on Friday, from mid-day until the afternoon [the time of ‘Asr].
Another saying is that the exalted angels stayed in prostration for 100 years, and another saying says that they stayed in prostration for 500 years.
satan did not prostrate and by way of arrogance, believed that he is superior to our master Adam and thought that for him, the command of prostrating [to our master Adam] is against logic [ma’aadh Allah, we seek Allah’s refuge from such] and by this false belief, he became kafir.
[Translator’s Note: Dear reader, we have a lot of people in these times too who like to pass ‘judgment’ on the wisdom behind divine commandments in this same arrogance like that of satan.
Muslims must be wary of such people. Applying one’s own faulty ‘judgment’ against the wisdom behind Allah’s manifest commandments is a certified character trait of satan himself. Muslims should NOT respect or hold ‘dialogue’ with those satanists who seek to give us their take on what according to them is right or wrong and how they think this or that law is a ‘better alternative’ than Islamic law, for example, those fools who try to negate Islam’s wisdom behind ordaining capital punishment for certain crimes. Muslims should be very harsh in dealing with such people and not just pretentiously ‘respectfully’ listen to such tripe.
Some of such people even call themselves ‘Muslim’ but they leave Islam and become kafirs when they say rubbish like “I do not agree with Islam’s prohibition of homosexuality” or “I think praying 5 times a day is too much, just praying once a day is enough”. Never forget dear reader, that as soon as one tries to suggest that he/she knows better than Allah’s commandments and possesses more wisdom than them, one leaves Islam and becomes a kafir. May Allah protect our faiths, aameen bi hurmati nabyyihil amiin.]
Mas-ala (Case): The ayah contains evidence that our master Adam, ‘alaihis salam, is superior to angels as it is them who were commanded to prostrate to him.
Mas-ala (Case): Arrogance (takabbur) is an extremely ugly thing and sometimes it can lead the arrogant person [the one practicing this sin] to kufr (disbelief). [Baidzaawiy and Al-Jamal]
[Translator’s Note: ibliis is the Arabic of satan’s name, lucifer. This name was given to him after he became a kafir. ibliis has its roots in the word “balasa”, meaning “deception”. his former name was ‘azaazeel. his kunniyah (kunniyah is a nick name assigned in Arab culture) is ‘abu murrah’, meaning ‘father of bitterness’.]
 – This refers to wheat or grapes and others. [Jalalayn]
 – The meaning of zdhulm (injustice) is ‘to place something outside of its assigned place’ and this is not allowed. And the ambiyaa (prophets) are ma’suum (protected from sin by Allah) and they do not commit sins. Here ‘zdhulm’ is used in a figurative sense [and the usage is from Allah Ta’ala].
Mas-ala (Case): Calling ambiyaa (prophets), ‘alaihimus salam, ‘zdhaalim’ (transgressors) is insulting them and kufr. The one who says it will become kafir. Allah Ta’ala is the Creator and The Owner of everything, He can say as He Wills, and in it is honor bestowed on them [due to His Commanding & Warning them, as is used in the verse]. How dare someone other than Him utter words of a degrading tone, and use The Almighty’s addressing of His slaves as an evidence for His own lack of respect [for prophets and those far exalted in status than their own selves]. We have been commanded ONLY to honor, respect, and exalt [the prophets] and this is COMPULSORY on us.
[Translator’s Note: Furthermore, the Quran itself testifies elsewhere that our master Adam only had a lapse and was not deliberate in his action. This is a sound evidence for his eminence, the exegete’s saying that the usage of ‘zdhulm’ in the discussed verse 35 of this surah is only figurative.
(وَلَقَدْ عَهِدْنَا إِلَىٰ آدَمَ مِن قَبْلُ فَنَسِيَ وَلَمْ نَجِدْ لَهُ عَزْمًا) (And indeed, before it, we gave Adam an emphatic command; then he forgot, and We did not find a deliberation from him. 20:115)
Please note that Allah is The One Who Knows everything. “Finding deliberation” is a figure of speech. The ‘emphatic command’ talked about here is the same command not to approach the tree, and this verse clearly states that our master Adam, ‘alaihis salam, forgot and it was not deliberately intended.]
 – satan somehow reached our master Adam and mother Hawwa (‘alaihumas salam) and said, ‘i will tell you the tree of khuld (everlasting)’. Our master Adam ‘alaihis salam refused. he said on oath that ‘i am your well-wisher’. He [our master Adam] thought that who would take a false by Allah Subhanahu wa Ta’ala. In the same vein, our mother Hawwa ate something from it, and then gave it to our master Adam, he too ate it. Our master Adam thought that the restriction of (لا تقـربـا) (do not approach/go near) is tanziihi (discouraged only) but not tahriimi (prohibitive), because if he would have thought it as tahriimi, he would definitely not have done as such, as prophets are ma’suum. Here our master Adam, ‘alaihis salam, lapsed in his ijtihad (deduction of laws) and a lapse in ijtihad is NOT sinfulness.
 – Our master Adam, and his wife Hawwa, and their offspring to be that they concealed in themselves, were commanded to go from jannah to the earth. Our master Adam, descended on earth, in the land of India in Sarandeep Island (modern day Sri Lanka) and our mother Hawwa descended in Jeddah (modern Saudi Arabia). [Khazen]
By the blessings granted to our master Adam, ‘alaihis salam, a pure fragrance was emerged forth from the plantations on earth. [Ruuh Al-Bayan]
 – This refers to the termination of the life span, that is, the time of death, and there is a glad tiding for our master Adam, ‘alaihis salam, that he is in this world only for this specified time frame and after that he has to return to jannah, and for his progeny, it is evidence for life of the hereafter, that the life in this world is for a specified time frame and after this life is over, they have to head towards the hereafter.
 – After arriving on earth, our master Adam, ‘alaihis salam, did not lift his head towards the sky for 300 years, out of shyness. Even though our master Dawuud, ‘alaihis salam, cried a lot [in fear of Allah] and his tears are more than the tears of all those on earth, our master Adam, ‘alaihis salam, cried so much that his tears were more than the tears of our master Dawuud, ‘alaihis salam, and those of all people on earth put together. [Khazen]
Tabarani, Haakim, Abu Na’iim, and Bayhaqiy have narrated marfoo’an (that is through a hadith directly traceable to our Master Rasulullah ﷺ) from our master ‘Ali Murtadza, radzi Allahu Ta’ala ‘anhu, that when our master Adam was reproached, he was overwhelmed by the desire of repentance. In that state of worry, he remembered, ‘At the time of my birth [i.e., creation], I lifted my head and saw that it is written on the ‘Arsh (The Throne) (لا الـه الا الله محمـد الرسـول الله) (There is no God except Allah, and Muhammad [ﷺ] is the Messenger of Allah). I understood, that in the court of the Almighty, no one has such a lofty standing as is bestowed on [our Master] Muhammad , that Allah Ta’ala has written his name next to His own name on the ‘Arsh.’ Therefore, in his dua, along with (رَبَّنَا ظَلَمْنَا أَنفُسَنَا وَإِن لَّمْ تَغْفِرْ لَنَا وَتَرْحَمْنَا لَنَكُونَنَّ مِنَ الْخَاسِرِينَ) (O our Lord, we have wronged our own selves, then if You do not forgive us and have mercy on us, then indeed we will be from those who have lost; 7:23) he also stated (أسئـلـك بـحـق محـمـد أن تغـفـر لـي) (as-aluka bi-haqqi Muhammadin an taghfira liy) (I ask you by the right [granted to] Muhammad, that you forgive me).
The narration by Ibn Mundhir contains the words (الـلـهم انـي اسـئـلـك بـجـاه مـحمـد عبـدك و كـرامـتـه علـيـك أن تـغـفـرلـي خـطيـئـتـي) (Allahumma inniy as-aluka bi-jaahi Muhammadin ‘abdika wa karaamatihii ‘alaika an taghfira liy khateei-atiy) (O Allah! I ask you by your special slave, Muhammad’s ﷺ lofty status and rank, and the grace that is bestowed upon him in Your Court, that You forgive me.) As soon as he [Adam, ‘alaihis salam] supplicated thusly, Allah Ta’ala granted him forgiveness.
Mas-ala (Case): From this narration [mentioned above] it is proven that it is permissible and the sunnah of Adam, ‘alaihis salam, to supplicate by the tawassul (intercession) of those acceptable in the Almighty’s Court, saying by the right granted to <name of person with great status> and by the status/rank granted to <name of person with great status>.
Mas-ala (Case): No one has any rights (haqq) on Allah Ta’ala, but by His grace and granting, He bestows rights on them, and it is these rights that He grants to them, by whose tawassul that we pray. These kinds of granted rights are proven by sahiih (authenticated) ahadiith, for instance as stated (مـن امـن بـالـلّـه و رسـولـه و اقـام الـصـلـوة و صـام رمـضـان كـان حـقـا عـلـى الـلّـه ان يـدخـلـه الـجـنـة) (The one who declared belief in Allah and His Messenger, and established salah, and fasted in Ramadzan, Allah’s Grace grants him the right to jannah.)
Our master Adam’s, ‘alaihis salam, repentance was accepted on the 10th of Muharram. At the time of leaving jannah, along with other blessings being confiscated, the Arabic language too was taken away from him. Instead of this, Syriac was bestowed on his blessed tongue. After the acceptance of his repentance, again the language of Arabic was granted. [Fath Al-‘Aziiz]
Mas-ala (Case): The base of tawbah (repentance) is turning towards Allah. It has three pillars: 1) admission of crime 2) sincere regret 3) commitment to forsake [the wrongful act]. If the sin is reversible, then it also needs to be reversed. For example, for the tawbah of the taarik as-salah (the one who deliberately misses salah), it is also necessary that he offer the qadza (that is offering the salah, after its time has passed) of the missed prayers.
After his [Adam, ‘alaihis salam] tawbah, our master Jibriil, ‘alaihis salam, announced Adam’s, ‘alaihis salam, khilaafah to all animals on earth, and delivered the command upon all of them to obey him [Adam ‘alaihis salam], and all of them accepted to obey him. [Fath Al-‘Aziiz]
 – This is a glad tiding for pious believers that at the time of the greatest trial, they shall have no fear, neither any grief in the hereafter, they shall enter jannah without any grief.