This book aims at familiarizing workers in the fields of special functions and allied topics of mathematical analysis with the theoretic aspects of single, double and triple integrals of I-Function of one variable. It also includes Fourier series, Laplace Transform and Multiple integral Transform of I-Function of one variable. Since the I-functions reduce, in special cases, to several simpler functions (special functions of Applied Mathematics and Mathematical Physics) it can nonetheless be used by workers in a number of other disciplines as a reference book for useful key formulas.