Two theta function identities and some eisenstein series identities of Ramanujan

In this paper we prove two general theta function identities by using the complex variable theory of elliptic functions. As applications, we provide completely new proofs of some Eisenstein series identities of Ramanujan by these two theta function identities and one famous identity of Ramanujan for the Rogers-Ramanujan continued fraction. We also derive two remarkable theta function identities relating to the modular equations of degree 5.