Michel Broué is a distinguished French mathematician specialising in algebra. He is known for his work on modular representations of finite groups (where a famous conjecture bears his name), on the "generic approach" to representations of finite reductive groups, as well as for work on related areas like cyclotomic Hecke algebras. During a career spanning half a century, he has been the editor-in-chief of the Journal of Algebra (2001-2017), the director of the Department of Mathematics and Computer Science of the École Normale Supérieure and the director of the Institut Henri Poincaré (1999-2009).

1 Prerequisites and Preliminaries.- Part I Rings and Modules.- 2 Rings, Polynomials, Divisibility.- 3 Polynomial Rings in Several Indeterminates.- 4 More on Modules.- 5 On Representations of Finite Groups.- Part II Integral Domains, Polynomials, Fields.- 6 Prime and Maximal Ideals, Integral Domains.- 7 Fields, Division Rings.- Part III Finitely Generated Modules.- 8 Integrality, Noetherianity.- 9 Finitely Generated Projective Modules.- 10 Finitely Generated Modules Over Dedekind Domains.- 11 Complement on Dedekind Domains.- Part IV Characteristic Zero Linear Representations of Finite Groups.- 12 Monoidal Categories: An Introduction.- 13 Characteristic 0 Representations.- 14 Playing With the Base Field.- 15 Induction and Restriction: Some Applications to Finite Groups.- 16 Brauer's Theorem and Some Applications.- 17 Graded Representations and Characters.- 18 The Drinfeld-Lusztig Double of a Group Algebra.