The word fiqh linguistically means understanding (fahm). In technical usage it means knowledge of the practical legislative rulings derived from their detailed evidences.

Its types: The scholars divide fiqh into seven types and they are:

1. al-ibaadaat (worship), those rulings connected to worshipping Allaah such as prayer and fasting
2. al-ahwaal al-shakhsiyyah (personal affairs) such as the rulings connected to the family, marriage and divorce
3. al-mu'aamalaat (dealings), those rulings that define and arrange relationships between people such as trade, contracts and so on.
4. al-ahkaam al-sultaaniyyah (rulership and governance), those rulings that arrange and organize the relationship between the ruler and the ruled.
5. al-uqoobaat (punishments), the rulings pertaining to prescribed punishments, retribution and reprimand, chastisement.
6. al-huqooq al-duwaliyyah (state rights), rules that define the relationship between an Islamic state with other states
7. al-aadaab (manners), rulings pertaining to manners, character, etiquette.

Note that there are other ways to divide fiqh into types and this is just one of them.

As for the stages of development of fiqh, they are divided by the scholars into the following:

1. The era of legislation (tashree') from the first year of prophethood to the death of the Messenger (sallallaahu alayhi wasallam) in 11H and its period is 23 years.
2. The era of the rightly guided caliphs from 11H to 40H and its period is 30 years.
3. The era of the younger Companions and senior Successors (taabi'een) to the commencement of the second century, from 41H to 100H and its length is 60 years.
4. The era of arrangement and compilation from the beginning of the second century to the middle of the fourth century, from 101H to 350H and its period is 250 years.
5. The era of blind-following from the mid-fourth century to the fall of Baghdad, from 350H to 656H, and its length is 306 years.
6. The era of stagnation from the fall of Baghdad to the present time, from 656H to now, around 780 years.

Note that there are other classifications of the various stages of the the development (and stagnation) of fiqh but the histories are generally approximate and similar.

Refer to (الملخصات الفقهية الميسرة) "Simple, Summarized Fiqh Principles" (Imaad Ali Jumu'ah, 1434H, Dar al-Nafaa'is).