Integral equations have proved itself as one of the most important branches of mathematics. In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign. There is a close connection between differential and integral equations, and some problems may be formulated either way. Integral equations can be divided into three main classes: linear integral equations, non-linear integral equations and singular integral equations. The present book is based on lectures given by the author to students of various colleges studying mathematics. In designing this book the author tried to select the most important mathematical facts and present them so that the reader could acquire the necessary mathematical conception and apply mathematics to other branches. This book consists of six chapters. Chapter 1, Integral Equations in Mathematics. Chapter 2 contains the resolvent kernel and the Neumann series. In chapter 3 , we will discuss Fredholm's Equations with degenerate kernels. Chapter 4 presents Volterra Integral Equation. Chapter 5 contains the classical Fredholm's theory. Chapter 6, contains Symmetric Integral Equations- Hermitian Kernels.