The probability Method has recently been developed intensively and become one of the most powerful and widely used tools applied in Combinatorics. The basic Probability Method can be described as follows: In order to prove the existence of a combinatorial structure with certain properties, we construct an appreciate probability space and show that a randomly chosen element in this space has the desired properties with positive probability. This method was initiated by Paul Erdos, who contributed so much to its development over the last fifty years.

In this one-semester course, we shall teach methods as well as topics in the Probability Method applicable to Combinatorics using the famous textbook by Alon and Spencer. For the part of methods, we will touch basic method, linearity of expectation, alterations, second moment, Local Lemma, correlation inequalities, martingales and tight concentration, the Poisson paradigm, pseudo-randomness etc. For the part of topics, we shall touch random graphs, circuit complexity, discrepancy, geometry, cods, games and entropy, de-randomization etc.