The book provides a systematic presentation of modern methods of studying nonlinear operator equations based on topological and geometric ideas. The book covers the following issues: methods of proving the solvability of equations , conditions of uniqueness of decisions and assessment of the number of decisions , Study of the structure of multiple solutions , Approximate methods of solving equations , methods of studying equations with parameters , Study of bifurcation of solutions , study of problems with continuums of solutions, etc. The applications to nonlinear integral equations, boundary problems for ordinary differential equations and partial differential equations, the theory of nonlinear oscillations. are indicated. The book is intended for specialists in the field of functional analysis and its applications.