The book is a compilation of more than 1,800 problems that have appeared on Berkeley's preliminary exams since 1977. It is an invaluable resource of problems and solutions for every mathematics student who plans to enter a Ph.D. program. Students who work through this book will develop problem-solving skills in areas such as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra. This new edition has been updated with the most recent exams, including those given during the Fall 2025 semester.