Literature
Silverman, Joseph H: The Arithmetic of Elliptic Curves. Graduate Texts in Mathematics Volume 106, 2009, Springer-Verlag New York. ISBN: 9780387094946.
Milne, James S: Abelian Varieties. Online notes, 2008. Electronic version can be found here:Abelian Varieties(Go to "Course Notes", click on "Abelian Varieties".)
Background Literature
Mumford, D.; with appendices by Ramanujam, C.P. and Manin, Y.: Abelian Varieties. Studies in mathematics (Tata Institute of Fundamental Research), 1974. ISBN: 0-19-560528-4.