These are the lecture notes for the first module of the course B9075 - TOPICS IN HOLOMORPHIC FUNCTION THEORY, for the master in Mathematics for Applications. The notes are work in progress.
In 1825, Augustin-Louis Cauchy (1789–1857) published "Mémoire sur les intégrales définies, prises entre des limites imaginaires", where his crucial and foundational view of holomorphic functions was laid down with details and applications. Since the course starts exactly 200 years from Cauchy's publication, it might be interesting to read something on Cauchy's contributions to complex analysis.