Since the concept of group was clarified by Evariste Galois in 1832 for the theory of equations, group theory has become a leading field in mathematics and spred its influence in many scientific domains. Felix Klein showed its dominant role in geometry; Joseph Fourier started representation theory, Sophus Lie introduced the continuous transformation groups. Group theory contributes decisively to physics (relativity, thermodynamics, elementary particles, field theory, quantum mechanics?) chemistry (christallography, molecular dynamics), and biology (braid groups and ADN).
Harish-Chandra, who started his research under P.A.M. Dirac, made considerable progress in representation theory of Lie groups. Then, R. -P. Langlands predicted a functoriality between deep questions in arithmetic on one side, and harmonic analysis on Lie groups on the other side. The power of this correspondence appears also in the recent proof by Wiles of the Last Fermat Theorem.
The preceding schools (every year since 1991, most of them supported by the European Community through HCM and TMR programs) were extremely positive. Bringing together students and post-docs from many European countries and even outside the European Community (Africa, America), these schools encourage cooperation and more balanced development inside Europe in the field of group theory. Moreover, a special effort is made to attract participants form less-favoured regions.
There are continuous requests for the notes of these Summer schools. Two sessions were published as books in the series Perspective of Mathematics.