Elliptic functions parametrize elliptic curves, and the
intermingling of the analytic and algebraic-arithmetic theory has
been at the center of mathematics since the early part of the
nineteenth century. The book is divided into four parts. In the
first, Lang presents the general analytic theory starting from
scratch. Most of this can be read by a student with a basic
knowledge of complex analysis. The next part treats complex
multiplication, including a discussion of Deuring's theory of
l-adic and p-adic representations, and elliptic curves with
singular invariants. Part three covers curves with non-integral
invariants, and applies the Tate parametrization to give Serre's
results on division points. The last part covers theta functions
and the Kronecker Limit Formula. Also included is an appendix by
Tate on algebraic formulas in arbitrary charactistic.
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