I'm looking for an introductive book on Modular Forms and their applications to Algebraic Geometry and Algebraic Number Theory.
Some Ideas?
Explaining you my prerequisites, I've a good knowledge of basic instruments of Algebra and Algebraic Geometry, but I need some explanations in geometrical facts about Riemann Surfaces and Advanced Complex Analysis...
On
Modular Forms A Classical Approach, by Henri Cohen and Fredrik Strömberg.
https://www.amazon.com/dp/0821849476
A recent book ( 2017 ) with lots of exercises, only prerequisite is complex analysis.
The first book you want to look at is Serre's "A course in arithmetic". THe second is the aptly named "A first course in modular forms"