These are the following types of tafsir:
a. Self Explanatory
The Qur'an is explained by referring only to other verses of the Qur'an with minimal reference to the Sunnah. The point of this is to introduce the student to rare words and grammar of certain ayat and rulings.
An example of this would be Adwa' ul-Bayan fi Idah il-Qur'an bil-Qur'an (10 vols.) by Muhammad Al-Amin ibn Muhammad Al-Mukhtar Ash-Shanqiti (d. 1393 AH (AD 1971).
This form of tafsir records the language of the Qur'an, how many times a particular word is used, where certain narratives or statements are repeated, expanded or alluded to for the reader to reference.
A reader of this will find that the author has gathered not just the verses but all the ahadith on the subject. He then sifts through, clarifying the sound from the suspect, the baseless form the trustworthy, the fabricated from the fair and the incidents of recitation.
Included in this will be asbab un-nuzul (the reason why an ayah was revealed), asbab ul-wurud (the reason for a hadith being said) and waqi`ah (incidents where an ayah that was revealed for one purpose might be used to answer more than one question on more than one occasion).
Jami` ul-Bayan wat-Ta'wil is one such example as well as Tafsir ul-Qur'an il-Azim (4 large vols.) by Imam Abul Fida' Isma`il Ibn Kathir 1 and Lubab ut-Ta'wil fi Ma`alam it-Tanzil (4 vols.) by Imam Al-Hussain Al-Baghawi. 2
This is a tafsir in order to know which certain ayat apply in fiqh, to one's particular madhhab or the discussion of all the madhhabs, detailing issues of consensus, preponderant agreement, difference of opinion and the authorities who declared it as such.
Examples of this would be Ahkam ul-Qur'an (4 vols.) by Al-Qadi Abu Bakr ibn Al-`Arabi, 3 Al-Muharrar ul-Wajiz fi Tafsir il-Qur'an il-`Aziz (4 vols) by `Abdul Haqq Ibn `Atiyyah 4 as well as Tafsir ul-Qur'an by `Izz ud-Din `Abdul `Aziz ibn `Abdus-Salam As-Sulami. 5
This is a tafsir in which the writer gives the commentary of a few sentences along with the reasons for revelation. This is designed to be a desktop reference manual or read along with other commentaries.
Expository examples would include `Ali ibn Ahmad Al-Wahidi's 6 Asbab un-Nuzul and Jalal ud-Din As-Suyuti and Al-Mahali's Al-Jalalayn.
Expository tafsirs will also give wise counsels, aphorisms and spiritual nuggets for the reader to take away.
If a reader or researcher wanted to study a very detailed issue that had occurred to his or her mind while reading the Jalalayn, then the other categories previously mentioned would have to be consulted, based on the subject.
The best expanded commentary on the Jalalayn is the Hashiyah of Imam Ahmad As-Sawi. 7 The best expository example of the Qur'an and the earliest is Tanwir ul-Maqbas.
This joins between all the types of tafsir mentioned above and gives the reader a thorough overview of the best of all subjects under each heading.
Examples of this include Al-Jami`u Li-Ahkam il-Qur'an (22 vols.) by Imam Abu `Abdullah Al-Qurtubi, 8 Al-Lubab fil `Ulum il-Kitab (20 vols.) Siraj ud-Din `Umar Ibn `Adil, 9 Rumuz ul-Kunuz fi Tafsir il-Kitab il-`Aziz (9 vols.) by Imam Ibn Rizqullah 10 and Zad ul-Masir fi `Ilm it-Tafsir (4 vols.) by Imam Ibn Al-Jawzi. 11