Contents -- Preface -- 1. The Basic Identity -- 1.1 Introduction -- 1.2 The generalized Ramanujan identity -- 1.3 The Weierstrass elliptic function -- 1.4 Notes -- 2. The Differential Equations of P, Q and R -- 2.1 Ramanujan's differential equations -- 2.2 Ramanujan's 1ψ1 summation formula -- 2.3 Ramanujan's transcendentals U2n and V2n -- 2.4 The imaginary transformation and Dedekind's eta-function -- 2.5 Notes -- 3. The Jordan-Kronecker Function -- 3.1 The Jordan-Kronecker function -- 3.2 The fundamental multiplicative identity -- 3.3 Partitions -- 3.4 The hypergeometric function 2F1(1/2, 1/2 -- 1 -- x): first method -- 3.5 Notes -- 4. The Weierstrassian Invariants -- 4.1 Halphen's differential equations -- 4.2 Jacobi's identities and sums of two and four squares -- 4.3 Quadratic transformations -- 4.4 The hypergeometric function 2F1(1/2, 1/2 -- 1 -- x): second method -- 4.5 Notes -- 5. The Weierstrassian Invariants, II -- 5.1 Parameterizations of Eisenstein series -- 5.2 Sums of eight squares and sums of eight triangular numbers -- 5.3 Quadratic transformations -- 5.4 The hypergeometric function 2F1(1/4, 3/4 -- 1 -- x) -- 5.5 The hypergeometric function 2F1(1/6, 5/6 -- 1 -- x) -- 5.6 The hypergeometric function 2F1(1/3, 2/3 -- 1 -- x) -- 5.7 Notes -- 6. Development of Elliptic Functions -- 6.1 Introduction -- 6.2 Jacobian elliptic functions -- 6.3 Reciprocals and quotients -- 6.4 Derivatives -- 6.5 Addition formulas -- 6.6 Notes -- 7. The Modular Function λ -- 7.1 Introduction -- 7.2 Modular equations -- 7.3 Modular equation of degree 3 -- 7.4 Modular equation of degree 5 -- 7.5 Modular equation of degree 7 -- 7.6 Modular equation of degree 11 -- 7.7 Modular equation of degree 23 -- 7.8 Notes -- Appendix A Singular Moduli -- A.1 Notes -- Appendix B The Quintuple Product Identity -- B.1 Notes -- Appendix C Addition Theorem of Elliptic Integrals.

Bibliography -- Index.