Counterexamples (in the usual mathematical sense) are powerful tools of mathematical theory. In this book the author gives more than 250 drawn from the whole field of probability theory and stochastic processes. The counterexamples are selected for their interest and for the importance of the theory they illustrate. Each section starts with a summary of definitions and main results, followed by counterexamples ordered by content and difficulty. Full references and additional sources are given. These counterexamples serve to illustrate the power, beauty and non-triviality of stochastics. They will provide new starting points for students and their teachers, as well as for researchers. The main results used in undergraduate and graduate courses in probability and stochastic processes are covered by these counterexamples. They will provide a useful source of illustrations and ideas for lecturers and examiners, as well as valuable supplementary reading for students.

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