Graduate school marks the first step toward a career in mathematics for young mathematicians. During this period, they make important decisions which will affect the rest of their careers. Here now is a detailed guide to help students navigate graduate school and the years that follow. In his inimitable and forthright style, Steven Krantz addresses the major issues of graduate school, including choosing a program, passing the qualifying exams, finding an advisor, writing a thesis, and getting that first job. As with his earlier guide, How to Teach Mathematics, he avoids generalities, giving clear advice on how to handle real situations. The book also contains a description of the basic elements of a mathematical education, as well as a glossary and appendices on the structure of a typical department and university and the standard academic ranks. Steven G. Krantz is an accomplished mathematician and an award-winning author. He has published 130 research articles and 45 books. He has worked in many different types of mathematics departments, supervised both masters and doctoral students, and is currently the Chair of the Mathematics Department at Washington University in St. Louis.