This new approach to mathematics --- the utilization of advanced computing technology in mathematical research --- is often called experimental mathematics. The computer provides the mathematician with a "laboratory" in which she can perform experiments --- analyzing examples, testing out new ideas, or searching for patterns. This book presents the rationale and historical context of experimental mathematics, and includes a series of examples that best portray the experimental methodology. For more examples and insights, the book, "Experimentation in Mathematics: Computational Paths to Discovery" is a highly recommended companion. .