— In these notes we present some basic results of the Theory of Curves over Finite Fields. Assuming a famous theorem of A. Weil, which bounds the number of solutions in a finite field (i.e., number of rational points) in terms of the genus and the cardinality of the finite field, we then prove several other related bounds (bounds of Serre, Ihara, Stohr-Voloch, etc.). We then treat Maximal Curve...
