I am very fascinated to publish this book. This book is nothing but a part of my research, which has been mentored by Prof. M. S. Chaudhary at the Department of Mathematics, Shivaji University, Kolhapur (M.S.), India in 2012. In this book I have presented analytical study of some integral transforms like the Sumudu transform, Elzaki transform, Mellin type integral transform and newly defined Hybrid Sumudu-Z transform. These transforms extended on the different spaces of generalized functions like space of pseudoquotients, space of Boehemians and developed their operational calculus on respective spaces. Also analytical investigations of properties of the hybrid Sumudu-Z transforms have been presented. Since this book is devoted to the operational calculus of integral transforms, so some applications are also presented which are elaborate the utility of our developed operational calculus. I strongly recommend that this book is very useful to students and research scholars of mathematics.