Definitions and basic properties -- Elementary examples -- A handle decomposition of the milnor fibre -- Generalized Lê-Iomdine formulas -- Lê numbers and hyperplane arrangements -- Thom’s a f condition -- Aligned singularities -- Suspending singularities -- Constancy of the Milnor fibrations -- Other characterizations of the Lê cycles.

This book describes and gives applications of an important new tool in the study of complex analytic hypersurface singularities: the Lê cycles of the hypersurface. The Lê cycles and their multiplicities - the Lê numbers - provide effectively calculable data which generalizes the Milnor number of an isolated singularity to the case of singularities of arbitrary dimension. The Lê numbers control many topological and geometric properties of such non-isolated hypersurface singularities. This book is intended for graduate students and researchers interested in complex analytic singularities.