The book entitled Integral equation and Transforms consists of eight chapters.This book contains preliminary concepts of integral equations, some problems which give rise to integral equations, conversion of ordinary differential equations into integral equations, classification of linear integral equations, integro-differential equations. Fredholm equations, degenerate kernels, Hermitian and symmetric kernels, the Hilbert-Schmidt theorem, Hermitization and symmetrization of kernels, solution of integral equations with green¿s function type kernels,types of Voltera equations, Resolvent kernel of Voltera equations, convolution type kernels,non- linear Voltera equations. Fourier integral equations, Laplace integral equations Hilbert transform, Fourier integral theorem, Fourier transform Fourier cosine and sine transform,the convolution integral, multiple Fourier transform, solution of partial differential equation by means of Fourier transform, the Laplace transform of some elementary functions, Laplace transform of derivatives, the convolution of two functions, inverse formula for Laplace transform and solutions of ordinary differential equations by Laplace transform.