The probabilistic method is now an integral part of combinatorics. We introduce the basic methods, including Markov’s and Chebyshev’s Inequalities, the local lemma, concentration of measure, the Chernoff Bound, martingales, Poisson approximation, and correlation inequalities. Two salient examples are the Hoeffding– Azuma Inequality and Janson Inequalities, and we give some brief applications of each result, including balancing vectors, random graphs, property B, concentration of chromatic number, and triangles in random graphs. The tools discussed in this chapter are used frequently in the material covered by this text.