Elliptic curves

Elliptic curves are the node of many branches in modern mathematics. The celebrated “Fermat’s Last Theorem” was proved (Wiles 1994) with the heavy use of the theory of elliptic curves. Elliptic curves over finite fields play an important role in modern cryptography. In this advanced lecture course we give a slow introduction to the world of elliptic curves, starting with the very basics of algebraic number theory and algebraic geometry. The lectures culminate in the Mordell-Weil theorem on the structure of the group of rational points on an elliptic curve defined over rational numbers.