M. : FASIS, 1996. — X+334 s. — (Mathematics Library.) Issue. 1). Caustics and wave fronts of ray systems have been studied for a long time. But it was not until recently that it was established that the features of systems) are governed by the theory of Euclidean reflection groups and Weyl groups of simple Lie algebras .. This is an unexpected and somewhat mysterious relationship between geometric optics. Variational Calculus and the Theory of Optimal Control , On the other hand, , and the theory of Lie group invariants and Lie algebras, algebraic topology and differential geometry , On the other hand, , led to significant progress in the development of wave propagation theory.