In 1961 the second author deliv1lred a series of lectures at Haverford Col- lege on the subject of "Rational Points on Cubic Curves. " These lectures, intended for junior and senior mathematics majors, were recorded, tran- scribed, and printed in mimeograph form. Since that time they have been widely distributed as photocopies of ever decreasing legibility, and por- tions have appeared in various textbooks (Husemoller 1], Chahal 1]), but they have never appeared in their entirety. In view of the recent inter- est in the theory of elliptic curves for subjects ranging from cryptogra- phy...