The present volume gather 15 research accounts given at the international conference on linear representations of finite groups (CIRM, Luminy, May 16-21, 1988). A point in common to most of those talks is the notion of block which originates in Brauer's theory of representations in characteristic $\neq 0$. One may find there numerous examples of the new lights recently shed on the notion of block. Speaking of problems, there are studies of Alperin's conjecture, the isomorphism problem for group algebras, blocks of ical groups. Apart from this main them of blocks, one may find also talks on other subjects : representations of finite groups of Lie type, linear codes, character theory.