目次

​Introduction.- Fundamentals of the theory of Lie algebras and root systems.- Definitions and examples.- Values at positive even integer points.- Convex polytopes and the rationality.- The recursive structure.- The meromorphic continuation.- Functional relations (I).- Functional relations (II).- Poincar´e polynomials and values at integer points .- The case of the exceptional algebra G2.- Applications to multiple zeta values (I).- Applications to multiple zeta values (II).- L-functions.-  Zeta-functions of Lie groups.- Lattice sums of hyperplane arrangements.- Miscellaneous results.