The purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes. There is particular focus on the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes.

This textbook is ideal for an undergraduate introduction to probability, with a calculus prerequisite. It is based on a course that the author has taught many times at Berkeley. The text's overall style is informal, but all results are stated precisely, and most are proved. Understanding is developed through intuitive explanations and examples. Graphs, diagrams, and geometrical ideals motivate results that might otherwise look likely purely formal manipulations.