This is the third edition of a popular UK textbook on stochastic processes. It has been updated with a new chapter on diffusion processes and Brownian motion, has extended material on birth and death processes and epidemics, plus new references throughout. The examples and exercises have all been expanded and improved. Praise for the second edition: "? a clear, easily understandable and rather short overview on stochastic processes. The different topics are motivated very well, there are many graphs and 50-theoretical and practical-examples. ? the book is written very carefully ? for beginners, one could not imagine a better book."-Dominik Wied, Statistical Papers (2011) 52 "? a good resource as a textbook or as a reference to complement other literature, especially with the examples and problems provided."-Biometrics, 67, September 2011