Integration with respect to the Euler characteristic and its applications

The notion of integration with respect to the Euler characteristic and its generalizations are discussed: integration over the infinite-dimensional spaces of arcs and functions, motivic integration. The author describes applications of these notions to the computation of monodromy zeta functions, Poincaré series of multi-index filtrations, generating series of classes of certain moduli spaces, and so on.
Bibliography: 70 titles.