Let me mention Nash's two famous contributions to game theory:
The notion of equilibrium of non cooperative games and a proof that every game has an equilibrium.
Nash's bargaining model, his proposed axioms that a solution should satisfy, and his solution. Links: (Nash's paper; a good wiki page (Hebrew))
More Let me copy my answer regarding Nash's work from a different question on the importance of Nash's work in game theory and economics.
Let me start with my own view:
The Nash equilibrium concept and the accompanying existence theorem is among the very few cornerstones in mathematical modeling of our reality .
Let me add a few more links. A paper by Ariel Rubinstein entitled "John Nash the master of economic modeling" and a document based on a seminar entitled: "The work of John Nash in Game theory." This includes the following quote from an earlier paper by Aumann.
Nash equilibrium is probably the main reason for the "game-theoretic revolution" in theoretical economics.
