Curves over finite fields form an interesting and accessible topic in its own right, but it finds applications in coding theory and cryptography. We shall treat the basic theory of curves over finite fields. Topics include ithe zetafunction, the Hasse-Weil bound and its improvements, maximal and optimal curves, curves with many points, asymptotics, towers, modular curves, supersingular curves, relation with coding theory.

References to the literature will be given at the beginning of the course.