What are Hanafi, Maliki, Shafi and Hanbali?

There are different approaches to the methodology used in fiqh to derive sharia from the Islamic sources. The main methodologies are:
The four classical Sunni schools are, in chronological order: the Hanafi school, the Maliki school, the Shafi’i school and the Hanbali school. They represent the generally accepted Sunni authority for Islamic jurisprudence.

Hanafi: (Turkey, Pakistan, the Balkans, Central Asia, Indian subcontinent, Afghanistan, China and Egypt)
Maliki: (North Africa, the Muslim areas of West Africa, and several of the Arab States of the Persian Gulf)
Shafi’i: (Arabia, Indonesia, Malaysia, Maldives, Egypt, Somalia, Eritrea, Ethiopia, Yemen and southern parts of India)
Hanbali: (Arabia)