Matthew C. H. Tointon is the Stokes Research Fellow at Pembroke College, Cambridge, affiliated to the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge. He has held postdoctoral positions at Homerton College, Cambridge, at the Université de Paris-Sud and at the Université de Neuchâtel, Switzerland. Tointon is the author of numerous research papers on approximate groups and he proved the strongest known results describing the structure of nilpotent and residually nilpotent approximate groups.

1. Introduction; 2. Basic concepts; 3. Coset progressions and Bohr sets; 4. Small doubling in abelian groups; 5. Nilpotent groups, commutators and nilprogressions; 6. Nilpotent approximate groups; 7. Arbitrary approximate groups; 8. Residually nilpotent approximate groups; 9. Soluble approximate subgroups GLn(C); 10. Arbitrary approximate subgroups of GLn(C); 11. Applications to growth in groups; References; Index.