This book is a guide for advanced mathematics learning. Each chapter is divided into five parts to help students grasp the direction and key points of learning and better understand the teaching materials. Each example question has a detailed answer, and some examples are selected from previous postgraduate entrance examinations or mathematics competition questions. The answers to the final test questions are also given, and some of the test questions are given detailed answers. This book can be used as a study guide for advanced mathematics in science and engineering, and as a reference material for teachers to prepare lessons and for students to take postgraduate entrance examinations.