That is the book in which there is no doubt by Shaykh Abdur-Rahman As-Sa'di

Allah says in the start of Surah Al-Baqarah:

"That is the book in which there is no doubt."

In his saying "That is the book" that is the great book in which contains information that the previous divine books doesn't contain of the great knowledge and the clear truth.

In his saying "In which there is no doubt" there is no doubt what so ever in any shape or form and the negation of doubt necessitates its opposite which is certainty. So this book contains knowledge, information that is certain and which removes and uplifts the doubts. The objective of the negation here is to establish a praiseworthy quality which must implicitly ellude to its opposite which is perfection because just merely negating something (without the implicit indication of perfection) is redundant and meaningless. Such a empty expression of negation doesn't contain any form of  praise.

Source:

Tayseer Al-Kareem Ar-Rahmaan Fi Tafsir Kalaam Al-Mannaan, p26

Imam Maalik's relationship with the Qur'aan by Shaykh Saalih Al-Usaymee

Amongst the best means of extracting guildence and precious gems from the Quraan is reciting to very frequently.
Imaam Ibn Abi Haatim in his Muqadimah Jarh Wa Ta'deel relates from Abdullah Ibn Wahb:

"We was astonished how Imam Maalik used extract from the Qur'aan so we asked his sister so she said when he used to enter his house he wasn't occupied with anything other than reciting the Quraan."

If a person reads the Quraan with the intention of extracting guildence he will attain understanding of it in abundance as a result of his intention.

Source: https://www.youtube.com/watch?v=aHW0sSvG3bE

The difference between the word Allah and Ilaah by Shaykh Muhammad Ali Saabooni

The word "Allah" indicates that the one who only has the right to be worshipped.

As for the word "Ilaah" indicates some who could have the right to be worshipped or not. So on one hand it may refer to Allah or to other than him as oppose to the word "Allah" then this restricts worship to him only.

Source: Safwa At-Tafaasir  Vol. 1, Pg 20

Tafsir of Ar-Rahman and Ar-Raheem by Shaykh Ibn Uthaymeen

Ar-Rahmaan (The most merciful)

It is a name meaning the one who is described with expansive, all encompassing mercy ie. the possessor of extensive mercy. Even the Arabic form upon which this name comes, concerning the rules of Arabic Conjugation indicates a sense of expansiveness, extensiveness and fullness. So one might say "A man is Ghadbaan." which is the same word pattern as Ar-Rahmaan this is not just the man is angry but is when he is filled up with anger. Any word that follows the word pattern of Fa'laan takes this connotation (like Ghadbaan, Ar-Rahmaan etc).
So Ar-Rahmaan means the one who has as his attribute very great and extensive mercy.

Ar-Raheem (The bestower of all Mercy)

It is a name meaning the one who bestows mercy on whomever he wills of his servants i.e one who is merciful to others. The Arabic form of the word indicates the occurrence of the action.

So here, mercy is one of Allah's characteristics or attributes proven by the name Ar-Rahmaan. Mercy also relates to his action bestowing mercy on the creation and this is indicated by his name
Ar-Raheem.

The particularities of Ar-Rahmaan

1. This is one of the names of Allah which exclusive to him nobody else may refer to themselves by Ar-Rahmaan.

2. Ar-Rahman refers to mercy in general (for the believers and the disbelievers).

3. Ar-Rahmaan is a description as well being a name of Allah.

4. Ar-Rahmaan refers to the one who has all-expansive mercy.

5.  Ar-Rahmaan refers to the attribute, adjective of mercy.

The particularities of Ar-Raheem

1. Ar-Raheem is one of the names of Allah

2. Ar-Raheem refers here to the action of mercy i.e granting mercy on others.

3. Ar-Raheem refers to the one who bestows mercy and is the source of all mercy.

4. The term Ar-Raheem can be applied to other Allah.

5. Ar-Raheem refers to the mercy that is specific to the believers