Timothy C. Burness is a Senior Lecturer in Pure Mathematics at the University of Bristol. His main area of research is in group theory; he is interested in simple groups, both finite and algebraic, with a particular focus on subgroup structure and representation theory. He has published numerous research articles in group theory, including two monographs in the Memoirs of the American Mathematical Society. He was formerly a Junior Research Fellow at St John's College, Oxford and a Lady Davis Fellow at the Hebrew University of Jerusalem. Michael Giudici is an Associate Professor at the University of Western Australia and is currently Deputy Director of the Centre for the Mathematics of Symmetry and Computation. His main research lies in permutation groups and the objects upon which they act. He has published numerous journal articles in group theory, graph theory and finite geometry. He previously held an Australian Research Fellowship and an Australian Postdoctoral Fellowship. In 2005 he received the Kirkman Medal from the Institute of Combinatorics and its Applications.

'This book should be an indispensable reference for anybody doing research, or wanting to do research, in this area. Even for nonspecialists, however, chapters 2 and 3 should be a useful source of information on classical groups.' Mark Hunacek, The Mathematical Gazette

• Preface; Notational conventions; 1. Introduction; 2. Finite classical groups; 3. Conjugacy classes; 4. Subspace actions; 5. Non-subspace actions; 6. Low-dimensional classical groups; Appendix A. Number-theoretic miscellanea; Appendix B. Tables; References; Index.

Timothy C. Burness is a Senior Lecturer in Pure Mathematics at the University of Bristol. His main area of research is in group theory; he is interested in simple groups, both finite and algebraic, with a particular focus on subgroup structure and representation theory. He has published numerous research articles in group theory, including two monographs in the Memoirs of the American Mathematical Society. He was formerly a Junior Research Fellow at St John's College, Oxford and a Lady Davis Fellow at the Hebrew University of Jerusalem. Michael Giudici is an Associate Professor at the University of Western Australia and is currently Deputy Director of the Centre for the Mathematics of Symmetry and Computation. His main research lies in permutation groups and the objects upon which they act. He has published numerous journal articles in group theory, graph theory and finite geometry. He previously held an Australian Research Fellowship and an Australian Postdoctoral Fellowship. In 2005 he received the Kirkman Medal from the Institute of Combinatorics and its Applications.

'This book should be an indispensable reference for anybody doing research, or wanting to do research, in this area. Even for nonspecialists, however, chapters 2 and 3 should be a useful source of information on classical groups.' Mark Hunacek, The Mathematical Gazette

• Preface; Notational conventions; 1. Introduction; 2. Finite classical groups; 3. Conjugacy classes; 4. Subspace actions; 5. Non-subspace actions; 6. Low-dimensional classical groups; Appendix A. Number-theoretic miscellanea; Appendix B. Tables; References; Index.

Timothy C. Burness is a Senior Lecturer in Pure Mathematics at the University of Bristol. His main area of research is in group theory; he is interested in simple groups, both finite and algebraic, with a particular focus on subgroup structure and representation theory. He has published numerous research articles in group theory, including two monographs in the Memoirs of the American Mathematical Society. He was formerly a Junior Research Fellow at St John's College, Oxford and a Lady Davis Fellow at the Hebrew University of Jerusalem. Michael Giudici is an Associate Professor at the University of Western Australia and is currently Deputy Director of the Centre for the Mathematics of Symmetry and Computation. His main research lies in permutation groups and the objects upon which they act. He has published numerous journal articles in group theory, graph theory and finite geometry. He previously held an Australian Research Fellowship and an Australian Postdoctoral Fellowship. In 2005 he received the Kirkman Medal from the Institute of Combinatorics and its Applications.

'This book should be an indispensable reference for anybody doing research, or wanting to do research, in this area. Even for nonspecialists, however, chapters 2 and 3 should be a useful source of information on classical groups.' Mark Hunacek, The Mathematical Gazette

• Preface; Notational conventions; 1. Introduction; 2. Finite classical groups; 3. Conjugacy classes; 4. Subspace actions; 5. Non-subspace actions; 6. Low-dimensional classical groups; Appendix A. Number-theoretic miscellanea; Appendix B. Tables; References; Index.