Types  of Fasting
Question

What are the categories of rulings on fasting?
Praise be to Allah.Types of fasting in Islam
The types of fasting in Islam are five: obligatory (wajib), forbidden (muharram), encouraged (mustahabb), disliked (makruh) and permissible (mubah). 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. 
Obligatory fasting 
·        The Ramadan fast
·        Making up missed Ramadan fasts
·        Expiatory fasts (expiation for accidental killing, expiation for zihar (a form of jahili divorce), expiation for having intercourse during the day in Ramadan, and expiation for breaking an oath)
·        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-Qiran), 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].
·        Fasting in fulfillment of a vow
Mustahabb (encouraged) fasting 
·        Fasting the day of `Ashura
·        Fasting the day of `Arafah
·        Fasting on Mondays and Thursdays each week
·        Fasting three days of each month
·        Fasting six days of Shawwal
·        Fasting most of the month of Sha`ban
·        Fasting the month of Muharram
·        Fasting alternate days – which is the best of fasting
All of these are proven in hasan and sahih hadiths, and may be found on this site. 
Makruh (disliked) fasting 
·        Singling out Friday for fasting – because the Prophet (peace and blessings of Allah be upon him) said: “Do not fast on a Friday unless you fast a day before or a day afterwards.” (Agreed upon)
·        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 Dawud, 2421; Ibn Majah, 1726; classed as sahih by al-Albani in Irwa al-Ghalil, 960.
Al-Tirmidhi said: “What is meant by its being makruh is that a man should not single out Saturday for fasting because the Jews venerate Saturday.”
Forbidden fasts 
·        Fasting on ‘Eid al-Fitr, ‘Eid al-Adha and the days of Tashriq, which are the three days after ‘Eid al-Adha.
·        Fasting on the “day of doubt” – which is the thirtieth of Sha`ban, if the sky was cloudy and the new moon could not be sighted. But if the sky was clear there can be no doubt.
·        Fasts observed by women who are menstruating and bleeding following childbirth.
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. 
References: 
1.     Al-Mawsu’ah al-Fiqhiyyah, 28/10-19
2.     Al-Sharh al-Mumti’, 6/457-483 
And Allah knows best.