Which are the different Schools of Economic Thought? It would be great to have a brief but comprehensive list of current (e.g. Austrian) and defunct (e.g Mercantilism) schools of thought in Economics. I think an ideal answer would include:


the defining features of the school, which enable it to differentiate it with the rest. 
major authors/writers behind the school.
key papers/books/textbooks presenting/defending the ideas of the school of thought.


Note: To order the discussion and avoid very lengthy answers, I suggest we have one school of thought per answer (like they do in other forums, like TeX).
Post-Keynesian

Post-Keynesianism (PK) is based on the criticism of the so called "Keynesianism", which according to PKs is not loyal to core Keynes ideas. As such, this school of thought aims to be called the "true" Keynesians.

The criticism starts with the workhorse model of Keynesianism, the IS-LM model, developed by Hick in a 1937's article, right after Keynes magnum opus. According to Minsky (a prominent PK), this is


  an article which ... misses Keynes’ point completely’ (Minsky, 1969, p. 225)


Later in life Hicks acknowledge this, by stating that his model


  was Walrasian rather than Keynesian in origin (Hicks, 1981, p. 142)


Given this background, PK has the following core features in its method:


emphasis on disequilibrium rather than equilibrium (as in IS-LM).
rejection of rational expectations. Agents can make inaccurate estimates of future based on present information without need to be either fully rational or incredibly naive.
against microfoundations. PKs argue that "emergent properties" of a system, arising from the interaction of individuals, means a system cannot be understood from a simple extrapolation of the properties of a few agents (e.g. representative firm and household).
the use of Leontieff (fixed proportion) production functions. PKs reject the marginalist theory, and argue that the latter is empirically inconsistent (e.g. Blinder, 1998).
Money is not neutral. This is a straightforward Keynesian argument, also present in IS-LM. Modern approaches highlight the crucial role of banks in endogenous money creation, which is not dependent on reserves (e.g. Moore, 1979).
Government has an important role in stimulating aggregate demand. Also in line with IS-LM, PKs argue that effective demand is what matters for economic activity. Say's law is therefore rejected.


Some early authors of this discipline are Michael Kalecki, Joan Robinson, Nicholas Kaldor, Luigi Pasinetti, and Piero Sraffa. More recent authors include Wynne Godley, Steve Keen, Frederic S. Lee, and Marc Lavoie.

A recent introduction to PK can be found in Godley and Lavoie (2007). There is also a very comprehensive two-volume Oxford Handbook of Post-Keynesian Economics.

Sources: own research, and Keen (2013).