C. Birkenhake/H. Lange: Complex abelian varieties.
Springer 2004, 660p. Eur 90.

S. Bosch/W. Lu''tkebohmert/M. Raynaud: Neron models.
Springer 1990, 320p. DM 158. A difficult book, gives a full proof of Neron's
existence theorem for models on an abelian variety. See the review by van der
Put. A simple definition of a model could be as follows: Let X be a variety
defined over the rationals. A model of X is a variety (scheme) defined over
the integers, which extended to the rationals gives a variety isomorphic to X.

16236 Daniel Bump/Alexander Pekker: On the dimension of the space of theta
functions. Proc. AMS 130/12 (2002), 3473-3481.

1744 Gary Cornell/Joseph Silverman (ed.): Arithmetic geometry. 
Springer 1986.

-5205 Gerd Faltings: Arithmetische Kompaktifizierung des Modulsraums der
abelschen Varieta''ten. SLN Math. 1111 (1985), 321-383.

J.-M. Fontaine: Il n'y a pas de varietŽ abelienne sur Z.
Inv. Math. 81 (1985), 515-538.

G. van der Geer: Hilbert modular surfaces.
Springer 1988, 290p. DM 148.

88 K. Hulek: Elliptische Kurven, abelsche Fla''chen und das Ikosaeder.
Jber. DMV 91 (1989), 126-147.

Klaus Hulek/Constantin Kahn/Steven Weintraub: Moduli spaces of abelian surfaces.
De Gruyter 1993, 350p. 3-11-013851-4. DM 168.

3593 Serge Lang: Introduction to algebraic and abelian functions. 
Springer 1982.

3605 Serge Lang: Abelian varieties. Springer 1983.

3146 Herbert Lange: Projective embeddings of abelian varieties.
Jber. DMV 93 (1991), 161-174.

Herbert Lange/C. Birkenhake: Complex abelian varieties. 
Springer 1992, 440p. 3-540-54747-9. DM 148. 
Should be self-contained and well-written.

Barry Mazur: Rational isogenies of prime degree.
Inv. Math. 44 (1978), 129-162.

David Mumford: On the equations defining abelian varieties I-III.
Inv. Math. 1 (1966), 287-354, 3 (1967), 75-135, 3 (1967), 215-244.
Very important papers.

Giuseppe Pareschi: Syzygies of abelian varieties.
Bull. AMS ... (ca. 2000), ...

5568 M. van der Put: Review of the book "Neron models" by
Bosch/Lu''tkebohmert/Raynaud. Jber. DMV 94 (1992), B 55-56.

Alain Robert: Introduction aux varietes abeliennes.
L'Ens. math. 28 (1982), 91-137.

H.P.F. Swinnerton-Dyer: Analytic theory of abelian varieties.
Cambridge UP 1974.