In this book, we have discussed Pochhammer’s symbol; Non-terminating, terminating and truncated generlaized hypergeometric series; Wright’s generalized hypergeometric function; Appell’s, Kampe de Feriet’s and Exton’s double hypergeometric functions; Lauricella’s tripple hypergeometric function; Srivastava’s general triple hypergeometric function; Multivariable hypergeometric function of Srivastava-Daoust; Some series identities; Hypergeometric forms; Some summation theorems associated with well-poised series and nearly-poised series of 2nd kind; Some transformations associated with Euler, Exton and Whipple; Normal forms; Some indefinite integrals and integral operators of functions. ***MAIN FINDINGS*** :: 1. Hypergeometric Solutions of Elliptic Type Single, Double Integrals of Ramanujan and others. 2. Some Transformation Formulae Associated with Multiple Hypergeometric Functions. 3. Hypergeometric Transformations Motivated by the Work of Bailey, Cayley and Orr. 4. Multiple Series...