The three main branches of economics currently popular in Western universities
are Classical/Neo-classical, Keynesian, and Monetarist.
Classical economics refers primarily to work before the 20th century by people such as Adam Smith, David Ricardo, and Jean-Baptiste Say. Neo-classical economists like Irving Fisher have updated their work.
Keynesian economics derives from the work of John Maynard Keynes. Some other key Keynesians (no pun intended) include Roy Forbes Harrod and Sir John Richard Hicks.
Monetarists include the likes of Milton Friedman and Friedrich August von Hayek - although they have had various disputes with one another.