The idea of this book is to provide an extensive description of classical complex analysis, where "classical" means that sheaf theoretical and cohomological methods are omitted. The first four chapters cover the essential core of complex analysis, presenting fundamental results. After this standard material, the authors advance to elliptic functions and elliptic modular functions, including a glimpse of the most beautiful results in this field. The book concludes with applications to analytic number theory, featuring notable highlights of this fascinating subject, such as the Prime Number Theorem. Great importance is placed on completeness; all necessary concepts are developed, requiring only minimal prerequisites (elementary facts of calculus and algebra). More than 400 exercises, including hints for solutions and many figures, make this an attractive resource.