Codes and modular curves

These lecture notes have been written for a course at the Algebraic Coding Theory (ACT) summer school 2022 that took place in the university of Zurich. The objective of the course propose an in-depth presentation of the proof of one of the most striking results of coding theory: Tsfasman Vlăduţ Zink Theorem, which asserts that for some prime power $q$, there exist sequences of codes over ${\mathbb{F}}_q$ whose asymptotic parameters beat random codes.