The theory of elliptic functions is the fairyland of mathematics. The mathe- mathematician who once gazes upon this enchanting and wondrous domain crowded with the most beautiful relations and concepts is forever captivated.

Upon first browsing through this field, observing the numerous links to the theory of functions of a complex variable, to the theory of partial differential equations, to number theory, and even to statistical mechanics, one may be led to feel that it is wholly confined within the domain of analysis. A closer examination will show that the ties with algebra and topology are equally strong, and perhaps, on the most fundamental level, even stronger. Further observation shows that this theory, with its natural extensions—the theory of Abelian functions and modular functions—penetrates into virtually every area of mathematics and indeed requires all of these areas for its fruitful study.

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