This book provides readers with guidance on the key contents of each chapter of the textbook. In addition to analyzing and answering the exercises in each chapter, a large number of exercises that are not in the textbook are added and the answers are given. The book consists of eight chapters: the basis of set theory, relations, functions, finite sets and infinite sets, algebraic systems, graph theory, mathematical logic, and discrete modeling. Except the eighth chapter, the rest chapters are composed of main contents, review points, basic concepts and precautions, detailed analysis of typical examples, exercises and solutions in related textbooks, and additional supporting exercises and solutions.