This book is concerned with subgroups of groups of the form GL(n,D) for some division ring D. In it the authors bring together many of the recent advances in the theory of skew linear groups. Some aspects of skew linear groups are similar to those for linear groups, however there are often significant differences either in the method of proof or the results themselves. Topics covered in this volume include irreducibility, unipotence, locally finite-dimensional division algebras, and division algebras associated with polycyclic groups. Both authors are experts in this area of current interest in group theory and algebraists and research students will find this an accessible account of the subject.