The theory of features of differentiable maps is a rapidly developing area of modern mathematics, which is a generalization of the study of functions to a maximum and minimum and has numerous applications in mathematics, natural science and technology (the so-called theories of bifurcations and catastrophes). The monograph is a continuation of the book of the same authors published by the publishing house in 1982. It is devoted to families of complex hypersurfaces, asymptotics of integrals of multidimensional methods of stationary phase and pass, applications of methods of algebraic geometry to the study of critical points of functions. For mathematicians - researchers, graduate students, as well as for specialists in the field of mechanics, physics, engineering and other sciences interested in theories of the features of differentiable maps .