Introductive Book on Modular Forms

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...

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"

• Thank you! Another related question: in this books there's something about the J-invariants? Do you have some references about them? – Sabino Di Trani Dec 15 '13 at 0:57
• Yes. Serre's book already talks about it (I think), and certainly Diamond does. – Igor Rivin Dec 15 '13 at 0:58
• "The second is the aptly named 'A first course in modular forms'" -- that made me smile, although I wholly agree with the recommendations! – David Loeffler Dec 16 '13 at 15:32

The book---"A first course in modular forms" by F. Diamond, J. Shurman is a good book to start to study classical modular forms. The advanced one--- "Modular forms" by Toshitsune Miyake is also a very good textbook to learn modular forms. Good luck.

• Velcome to the site! – kjetil b halvorsen Jun 5 '14 at 19:37

Step $$0$$: J W Brown & R V Churchill - Complex Variables and Applications [→];

Step $$\frac12$$: E Freitag & R Busam : Complex Analysis [→];

Step $$1$$: E Freitag - Complex Analysis 2 [→].

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.