Kilford’s Modular Forms, A classical and computational introduction
There are a lot of excellent books on the theory of modular forms. Kilford,’s book Modular forms, A classical and computational introduction, by Imperial college press is definitely one of them. Chapter 1-4 cover the basic theory of the modular forms, at the general setting. Chapter 5 covers interesting applications, among them are approximating of pi, quadratic forms, Picard’s little theorem, Fermat’s Last theorem. The book is very pleasant to read. Suitable for any graduate students or mature undergrad who want to learn more about modular forms. Interesting computations are mentioned throughout the book. Although the title mention about computation. The computer related material is only mentioned in chapter 7.
I strongly recommend this book to anyone who wants to learn modular forms. I will also suggest this book as the first modular forms book to any students.
In below is also a list of books that cover classical theory of modular forms (the list is not intended to be complete, and are not in particular order)
The 1-2-3 of modular forms (chapter 1)
Serre, A Course in Arithmetic
Ogg, Modular forms and Dirichlet Series
Diamond, Shurman, A first course in modular forms
Iwaniec Topics in Classical automorphic forms
Bump, Automorphic forms and Representations (Chapter 1)
Miyake, Modular forms
