The book is based on lecture material read by students of the second year of the Faculty of Physics of Moscow State University . Considered: the theorem of the existence of eigenvalues and eigenfunctions of a homogeneous Fredholm integral equation of the second kind, decomposability by eigenfunctions, the SturmLiouville problem, Fredholm non-homogeneous equations of the second kind, equations of the Volterra type . Fredholm's equations of the first kind are considered as an incorrectly set task, in connection with which the basics of the regularizing algorithm A. are set out. N. Tikhonova . Numerical methods for solving integral equations. Some questions of the theory of integro-differential equations. are also presented. The textbook is intended for students of mathematical and physical specialties of universities .