This book contains several new modular equations in the form of Schläfli involving two moduli and four moduli. These modular equations complement to the works of Srinivasa Ramanujan and Schläfli. These modular equations were recorded by Ramanujan in his notebooks. In Chapter 3 we have constructed some modular equations of degree two in the spirit of Ramanujan and their applications to continued fractions have been given. Some application of the modular equations, class invariants and singular moduli are also established here. In the last Chapter, a continued fraction of Ramanujan and associated theta function identities have been investigated.