Praise be to Allah.
The categories of rulings are five: obligatory (waajib), forbidden (muharram), encouraged (mustahabb), disliked (makrooh) and permissible (mubaah). These five rulings have been narrated with regard to fasting. We cannot list everything that comes under each of these rulings, but we will mention what we can.
1 – Obligatory fasts
(i)The Ramadaan fast
(ii)Making up missed Ramadaan fasts
(iii)Expiatory fasts (expiation for accidental killing, expiation for zihaar (a form of jaahili divorce), expiation for having intercourse during the day in Ramadaan, and expiation for breaking an oath)
(iv)Fasting for the pilgrim who does tamattu’ in Hajj if he does not have a sacrificial animal. “and whosoever performs the ‘Umrah in the months of Hajj, before (performing) the Hajj, (i.e. Hajj-at-Tamattu‘ and Al-Qiraan), he must slaughter a Hady such as he can afford, but if he cannot afford it, he should observe Sawm (fasts) three days during the Hajj and seven days after his return (to his home)” [al-Baqarah 2:196 – interpretation of the meaning].
(v)Fasting in fulfilment of a vow
2 – Mustahabb (encouraged) fasts
(i)Fasting the day of ‘Ashoora’
(ii)Fasting the day of ‘Arafah
(iii)Fasting on Mondays and Thursdays each week
(iv)Fasting three days of each month
(v)Fasting six days of Shawwaal
(vi)Fasting most of the month of Sha’baan
(vii)Fasting the month of Muharram
(viii)Fasting alternate days – which is the best of fasting
All of these are proven in hasan and saheeh ahaadeeth, and may be found on this site.
3 – Makrooh (disliked) fasts
(i)Singling out Friday for fasting – because the Prophet (peace and blessings of Allaah be upon him) said: “Do not fast on a Friday unless you fast a day before or a day afterwards.” Agreed upon
(ii)Singling out Saturday for fasting – because the Messenger (peace and blessings of Allaah be upon him) said: “Do not fast on Saturdays apart from days when you are obliged to fast, even if one of you cannot find anything other than grape stalks or the bark of a tree (to suck on, to make sure that he is not fasting).” Narrated by al-Tirmidhi, 744, who classed it as hasan. Also narrated by Abu Dawood, 2421; Ibn Maajah, 1726; classed as saheeh by al-Albaani in Irwa’ al-Ghaleel, 960.
Al-Tirmidhi said: What is meant by its being makrooh is that a man should not single out Saturday for fasting because the Jews venerate Saturday. End quote.
4 – Forbidden fasts
(i)Fasting on Eid al-Fitr, Eid al-Adha and the days of Tashreeq, which are the three days after Eid al-Adha.
(ii)Fasting on the “day of doubt” – which is the thirtieth of Sha’baan, if the sky was cloudy and the new moon could not be sighted. But if the sky was clear there can be no doubt.
(iii)Fasts observed by women who are menstruating and bleeding following childbirth.
5 – Permissible fasts – these are fasts that do not come under any of the four headings mentioned above.
What is meant by permissible here is that there is no report enjoining or forbidding fasting on this day in particular, such as Tuesdays and Wednesdays, even though in principle, observing a voluntary fast is an act of worship that is encouraged.
See al-Mawsoo’ah al-Fiqhiyyah, 28/10-19; al-Sharh al-Mumti’, 6/457-483
And Allaah knows best.