The manual summarizes the main sections of Fredholm's theory of integral equations. The main attention is paid to issues related to the types of equations and methods for solving them. The existence and uniqueness theorem of the solution and a number of other most important theorems are considered. Examples with solutions are given for each type of equations and methods of their solution considered in the manual, in the last paragraph a list of problems for independent solution is given. The manual is intended for students of the specialty "Applied Mathematics and Computer Science," can be used by students of specialties: "Mathematics," "Mathematical Support and Administration of Information Systems," etc.