C. M. Campbell is Honorary Reader in the School of Mathematics and Statistics at the University of St Andrews. M. R. Quick is Senior Lecturer in the School of Mathematics and Statistics at the University of St Andrews. E. F. Robertson is Emeritus Professor in the School of Mathematics and Statistics at the University of St Andrews. C. M. Roney-Dougal is Professor of Pure Mathematics in the School of Mathematics and Statistics at the University of St Andrews. D. I. Stewart is Reader in the Department of Mathematics at the University of Manchester.

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• Introduction; 1. Finite group schemes Michel Brion; 2. Algorithms for polycyclic groups Bettina Eick; 3. The spread of finite and infinite groups Scott Harper; 4. Discrete subgroups of semisimple Lie groups, beyond lattices Fanny Kassel; 5. Complete reducibility and subgroups of exceptional algebraic groups Alastair J. Litterick, David I. Stewart and Adam R. Thomas; 6. Axial algebras of Jordan and Monster type Justin McInroy and Sergey Shpectorov; 7. An introduction to the local-to-global behaviour of groups acting on trees and the theory of local action diagrams Colin D. Reid and Simon M. Smith; 8. Finite groups and the class-size prime graph revisited Víctor Sotomayor; 9. Character bounds for finite simple groups and applications Pham Huu Tiep; 10. Generalized Baumslag–Solitar groups: a topological approach Mathew Timm.