The revised and expanded edition of this textbook presents concepts and applications of random processes with the addition of material on biological modeling. While still treating many problems in fields such as engineering and mathematical physics, the book also focuses on the topics of cancerous mutations, influenza evolution, drug resistance, and immune response. Discrete-Time Markov Chains -- Stationary Distributions of a Markov Chain -- Continuous-Time Birth and Death Markov Chains -- Percolation -- A Cellular Automaton -- Continuous-Time Branching Random Walk -- The Contact Process on a Homogeneous Tree -- Appendix: Some Facts About Probabilities on Countable Spaces -- Applications to Population Biology.- References.