Nowadays, almost everyone agrees that some knowledge of algebra is necessary. Algebra is a subject which deals with numbers, polynomials, matrices, transformations and their operations, as well as groups, rings, fields and modules. Modern algebra is also called abstract algebra. French mathematician E. Galois (1811-1832) who invented group and is regarded as the founder of modern algebra used the idea of group in a problem using radicals to solve algebraic equations. This book consists of five chapters. Chapter one includes some basic concepts and preliminary results. Chapter two is consisting of group theory, especial finite group theory. Some basic facts about rings will be introduced in Chapter three. Also principal ideal rings and Euclidean rings are contained in Chapter three. Chapter four is consisting of field theory and modules, especially finite extensions and finite fields. Elementary character theory will be introduced in Chapter five. Furthermore, some problems with solutions are provided after each chapter. The author is very thankful to Prof. D. White of Kent State University for giving lectures on Finite Group Theory while the author was visiting this university. The author is very grateful for the support of programs of Henan University of Technology (2024PYJH019) and Education Department of Henan Province (YJS2022JC16). My colleagues Donghao Li, Yuanxiao Li, Qingyun Meng and Yulei Wang are the associate editors of this book. However, none of these people is responsible for any typos or mathematical errors in this book. There must exist some errors and typos in this book due to time. When you find them, please let me know.