The authors successfully bridge the gap from foundational concepts to current research. Starting from Weierstrass's work, they discuss elliptic curves and complex multiplication. The section on elliptic modular forms can also be read independently. For the first time in textbook form, a proof of Siegel's main theorem for elliptic modular forms is presented. It includes detailed proofs and numerous exercises. This book develops the classical theory of elliptic functions and modular forms. The section on elliptic modular forms covers fundamental areas and dimension determination, as well as a chapter on Hecke operators and Dirichlet series with functional equations. Great emphasis is placed on theta series.