Madhab, or Islamic Jurisprudence, refers to the schools of Hadith and sharia interpretation that arose in the first 150 years of the Islamicate  cc 650-800.Literally referring to schools, the Madhabs were formed from the instruction of these early Imams who studied Hadiths and interpreted and transmitted them to their students. Originally in the late 8th and early 9th centuries there were many schools of Hadith interpretation, however they soon became consolidated into four paths of thought , named after the Imams who are credited with starting them.
The four main paths of thought are Hanafi,Maliki,Shafi'i,Hanbali. Contemporary to these four main paths several Shi'ite variants formed, which are still present to this day. The most well known of the Shi'ite variants are the Jariri's and the Zaidi's.
Formed by the Imam Abu Hanifa Ibn Thabit, who lived from 699-767, the Hanafi Madhab asserts the role of reason and liberal comparison. Hanifa was the first of the four Madhabs to form. Hanifa jurisprudence is most common in those areas formerly ruled by the Ottoman and the Mughal Empires which adopted the Hanafi Madhab as their official school of thought.
Formed by the Imam Malik Ibn Abbas, whose Al-Mutawanna and Mudawanna are the earliest Islamic legal texts extant, this Madhab relies on the Quran and authenticated Hadith in a strictly literal and conservative fashion. This Madhab is most predominant in North Africa, Morocco being the birth place of Ibn Abbas.
The Shafi'i madhab was formed by Imam Sahfi'i who coincidentally created "shafi'i's" law of hadith interpretation which asserted that only Hadith directly traced to Muhammad were valid. Shafi'i's law is considered the standard in modern medieval and modern Hadith scholarship. Shafi'i's madhab asserted the roles of analogy and consensus in reasoning. Ijma, and Qiyas, consensus of the scholars , and analogical reasoning based on Quran and Hadith come from this time. Shafi'i's school attempted to subvert the role of private judgement and replace it by precedent. This Madhab is most commonly found in northeastern Africa, Southeastern Asia, and in Southern Arabia.
The Hanbali Madhab is similar to both the Shafi'i and Maliki paths of thought. The emphasis is on judgement derived from precedents derived from Hadith and Sunnan gathered from the first three generations of Muslims.
Others : Jariri, Zaidi etc & etc
- Marshall Hodgeson, Venture of Islam