Abbas - Tanwîr al-Miqbâs min Tafsîr Ibn ‘Abbâs
And on his authority he related from Ibn 'Abbas regarding the saying of Allah, Exalted is He: (Alif. Lam. Mim.) that he said: 'Allah informed us about the story of the delegation of Najran; it is also said that this is an oath by which Allah swore that He is One and that He has neither progeny nor partner.
(Allah! La ilaha illa Huwa, Al-Hayyul-Qayyum) in the Tafsir of Ayat Al-Kursi. Allah's statement,
نَزَّلَ عَلَيْكَ الْكِتَـبَ بِالْحَقِّ
(It is He Who has sent down the Book to you with truth, ) means, revealed the Qur'an to you, O Muhammad, in truth, meaning there is no doubt or suspicion that it is revealed from Allah. Verily, Allah revealed the Qur'an with His knowledge, and the angels testify to this fact, Allah is sufficient as a Witness. Allah's statement,
مُصَدِّقاً لِّمَا بَيْنَ يَدَيْهِ
(Confirming what came before it) means, from the previous divinely revealed Books, sent to the servants and Prophets of Allah. These Books testify to the truth of the Qur'an, and the Qur'an also testifies to the truth these Books contained, including the news and glad tidings of Muhammad's prophethood and the revelation of the Glorious Qur'an.
(And He sent down the Tawrah) to Musa (Musa) son of `Imran,
(And the Injil), to `Isa, son of Mary,
(Aforetime) meaning, before the Qur'an was revealed,
(As a guidance to mankind) in their time.
(And He sent down the criterion) which is the distinction between misguidance, falsehood and deviation on one hand, and guidance, truth and piety on the other hand. This is because of the indications, signs, plain evidences and clear proofs that it contains, and because of its explanations, clarifications, etc.
إِنَّ الَّذِينَ كَفَرُواْ بِأيَـتِ اللَّهِ
(Truly, those who disbelieve in the Ayat of Allah) means they denied, refused and unjustly rejected them,
لَهُمْ عَذَابٌ شَدِيدٌ
(For them there is a severe torment) on the Day of Resurrection,
(And Allah is All-Mighty) meaning, His grandeur is invincible and His sovereignty is infinite,
(All-Able of Retribution.) from those who reject His Ayat and defy His honorable Messengers and great Prophets.
Maududi - Sayyid Abul Ala Maududi - Tafhim al-Qur'an
Alif Lām Mīm His saying “Alif” alludes to His being sufficient for you in all of your states. You are captive to heedlessness and have not found the way to right action and thinking. He is the One who sets in motion what restores you and is solely sufficient for you in what helps you. Without your asking-and even without you knowing your own state-He suffices for you even if you do not perceive it. He gives to you without your seeking. The Lām alludes to His kindness luṬf to you at the most subtle and hidden level so much so that the locus of favor by which He strengthens you is not apparent to you. The Mīm alludes to the harmony muwāfaqa of the stream of the [divine] determination of events taqdīr with the circumstances requested by the friends. Nothing in the world moves no particle appears unless it is an occasion of good pleasure with respect to them. It would not be going too far to say that in His words “Every day He is upon some matter” [55:29] the “matter” is an actualization of what the friends desire. It is said that by listening to these disconnected letters [Alif Lām Mīm] which are contrary to the ordinary customs of human discourse every concept disappears from the hearts whether it be a known written customary or imagined thing and whether it arises from necessity Ḍarūra sensory perception ḥiss or independent reasoning ijtihād. When the hearts are emptied of imagined and known concepts and the innermost selves are purified of customary and familiar things the name Allāh comes to a heart sanctified from everything other [than Him] and to an innermost self purified of every mode [of inquiry] kayf.