Structure Theory for Canonical Classes of Finite Groups The F hypercentre and its generalizations Groups with given systems of X permutable subgroups Between complement and supplement Groups with given maximal chains of subgroups Formations and Fitting classes This book offers a systematic introduction to recent achievements and development in research on the structure of finite non simple groups the theory of classes of groups and their applications. In particular the related systematic theories are considered and some new approaches and research methods are described e.g. the F hypercenter of groups X permutable subgroups subgroup functors generalized supplementary subgroups quasi F group and F cohypercenter for Fitting classes. At the end of each chapter we provide relevant supplementary information and introduce readers to selected open problems