The manual introduces the concept of an integral equation, the theorem of the existence of eigenvalues ​ ​ and eigenfunctions of a homogeneous Fredholm integral equation of the second kind. The questions of decomposability by eigenfunctions, the Sturm-Liouville problem, inhomogeneous integral Fredholm equations of the second kind, Volterra-type equations are considered. The Fredholm integral equations of the first kind are considered as an incorrectly posed problem, in connection with which the foundations of the regularization algorithm of A.P. Tikhonov are presented. Some information is provided on numerical methods of theories of integral equations. Some questions of the theory of integro-differential equations are also presented. For university students studying in the specialties "Physics" and "Applied Mathematics."