The book focuses prominently to present the elements of integral transforms especially as canonical cosine and canonical sine transforms in form suitable for the use of research.The aim has been to give information through systematic introduction to the subject. All significant results are stated as theorems, and proofs are given where it is necessary. There is also emphasis on properties of equations and their solutions in this book.This book is a result of my sincere endeavors while preparing this book excellent texts have been followed which are referred to in the bibliography. The attempts have been made to maintain the usual notations that are often referred to as standard notations in mathematics.