In this course, the student will delve deeper into the study of advanced topics in complex analysis of sequences and series, study their divergence and convergence, important theories to study their properties, and study complex integration in a detailed manner with several important theories such as Cauchy's theory of integration and Cauchy's theorem for integration - path independence theorem - loop theorem - Cauchy's formula theorem as well Taylor and Laurent theories and the use of Laurent's theory in the classification of tensile points.