Accompanied by more than 1,000 examples and exercises, this comprehensive, classroom-tested text presents numerous theories, techniques, and methods used for analyzing algorithms. It includes basic material on combinatorics and probability that can be used for students with weak backgrounds. It presents information on asymptotics not usually found in similar books, including Rice's method, the Euler and Boole summation formulas, and recurrences. The author offers tutorials throughout the text on topics as diverse as continued fractions, functions of a complex variable, numerical calculations, and Stieltjes integration. An appendix contains a comprehensive collection of useful formulas.