The subject of elliptic curves is one of the jewels of nineteenth-century mathematics, originated by Abel, Gauss, Jacobi, and Legendre. This book presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more recent and modern developments. The treatment combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetics. Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the subject for graduate students and researchers in mathematics and physics. The many exercises with hints scattered throughout the text give the reader a glimpse of further developments.

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