Some theorems on the Rogers-Ramanujan continued fraction in Ramanujan's lost notebook

In his first two letters to G. H. Hardy and in his notebooks, Ramanujan rec orded many theorems about the Rogers-Ramanujan continued fraction. In his l ost notebook, he offered several further assertions. The purpose of this pa per is to provide proofs for many of the claims about the Rogers-Ramanujan and generalized Rogers-Ramanujan continued fractions found in the lost note book. These theorems involve, among other things, modular equations, transf ormations, zeros, and class invariants.