This book gives a systematic introduction to the theory of classes of groups,including research subjects,major(recent)research achievements,and directions for future research.It clearly and concisely treats a wealth of topics,such as a brief introduction to the fundamental knowledge of group theory;the classical part of the theory of classes of groups covering mainly F-covering subgroups,F-projectors,F-injectors and F-normalisers;local formations;Schunck classes;Fitting classes;properties of local formations;formation constructions of finite groups and related applications;and the algebra of formations.