A comprehensive compilation of approximately 900 problems which have appeared on the preliminary exams in Berkeley, and as such is designed to be a source of problems and solutions for mathematics students embarking on PhD programmes. The work is designed to develop problem-solving skills in areas such as real analysis, multi-variable calculus, differential equations, metric spaces, complex analysis, algebra and linear algebra. The problems are organized by subject and ordered by increasing level of difficulty, while tags with the exact examination year provide the opportunity to rehearse complete mock exams. The text also includes statistics on passing scores.