Elliptic Curves and Modular Forms

Iwasawa Theory of Elliptic Curves - Lecture notes and surveys by Ralph Greenberg, University of Washington (PS).
http://www.math.washington.edu/~greenber/research.html

An Elementary Introduction to Elliptic Curves - By Len Charlap, David Robbins and Raymond Coley. Downloadable text in PostScript (.ps) format.
http://www.idaccr.org/reports/reports.html

Modular Forms and Hecke Operators - Notes by William A. Stein of a course by Ken Ribet.
http://modular.fas.harvard.edu/MF.html

Papers by Richard Borcherds - Including proof of the Moonshine Conjecture (TeX,DVI,PDF).
http://math.berkeley.edu/~reb/papers/

A Proof of the Full Shimura-Taniyama-Weil Conjecture - Article by Henri Darmon on the completion of the proof by Wiles, Breuil, Conrad, Diamond and Taylor. [PDF]
http://www.ams.org/notices/199911/comm-darmon.pdf

14H52: Elliptic Curves - From the Known Math series.
http://www.math.niu.edu/~rusin/known-math/index/14H52.html

Elliptic Curves - Links to research papers maintained by Stéfane Fermigier.
http://www.fermigier.com/fermigier/elliptic.html.en

History of Elliptic Curve Rank Records - A table up to rank 24 compiled by Andrej Dujella.
http://www.math.hr/~duje/tors/rankhist.html

Arithmetic of Cuves - Papers and surveys by Ed Schaefer.
http://math.scu.edu/~eschaefe/nt.html

Elliptic Curves Handout - Syllabus and detailed reading list by Miles Reid, University of Warwick.
http://www.maths.warwick.ac.uk/~miles/MA426/

Mathematical Things - Tom Womack's pages address many elliptic curve subjects, including curves of given rank and small conductor, Mordell curves of large rank, and interesting torsion groups.
http://tom.womack.net/maths/maths.htm

Recent Progress in the Theory of Elliptic Curves - An abstract to Henri Darmon's and Bertolini's work, which approaches a p-adic variant of the Birch - Swinnerton-Dyer conjecture, for curves of rank higher than one.
http://www.cms.math.ca/CMS/Events/winter98/w98-abs/node2.html

Rational Points on Elliptic Curves - A course by Jerrold Tunnell. An introduction to rational points on elliptic curves through examples.
http://www.math.rutgers.edu/~tunnell/math574.html

Counting Points on Elliptic Curves - Robert Harley, Pierrick Gaudry, François Morain and Mireille Fouquet have established new records for point counting in characteristic 2, using a new algorithm by to Takakazu Satoh.
http://www.math.jussieu.fr/~fouquet/elliptic.html

On 5 and 7 Descents for Elliptic Curves - Tom Fisher's Ph.D. thesis (Cambridge, 2000) in DVI and PS format.
http://www.dpmms.cam.ac.uk/~taf1000/thesis.html

ECMNET - The ECMNET Project to find large factors by the Elliptic Curve Method, mainly Cunningham numbers.
http://www.loria.fr/~zimmerma/records/ecmnet.html

Elliptic Curves with H. A. Verrill - Lecture notes and resources by Helena Verrill, Louisiana State University, 2004.
http://www.math.lsu.edu/~verrill/teaching/math7280/index.html

Modular Forms Course - Notes of a 1996 Berkeley course of Ken Ribet's on modular forms and Hecke operators.
http://modular.fas.harvard.edu/Tables/Notes/

Prime Values of Elliptic Divisibility Sequences - By Graham Everest.
http://www.mth.uea.ac.uk/~h090/primeEDS.html

The Birch and Swinnerton-Dyer Conjecture - A Clay Mathematics Institute Prize problem, with description by Andrew Wiles [PDF] and lecture by Fernando Rodriguez-Villegas [.ram].
http://www.claymath.org/millennium/Birch_and_Swinnerton-Dyer_Conjecture/

Elliptic Curves and Formal Groups - Lecture notes from a seminar J. Lubin, J.-P. Serre and J. Tate.
http://www.ma.utexas.edu/users/voloch/lst.html

Elliptic Curves and Cryptology - Marc Joye's list of elliptic curve resources includes people, books, and links. Many preprints are available from the site.
http://www.geocities.com/marcjoye/biblio_ell.html

Elliptic Curves II - Lecture notes by Johan P. Hansen.
http://home.imf.au.dk/matjph/Ell-E99.html

Joseph Silverman - Includes errata for his books Rational Points on Elliptic Curves and Advanced Topics in the Arithmetic of Elliptic Curves.
http://www.math.brown.edu/~jhs/

Kolyvagin Seminar - A semester-long seminar studying Kolyvagin's application of Euler systems to elliptic curves. Includes extensive lecture notes in PostScript or DVI format.
http://math.berkeley.edu/~osserman/seminar/

Elliptical Curve Cryptography - Explains the difference between an elliptical curve and an ellipse. Discusses fields, applications, choosing a fixed point, and related topics.
http://www.cryptoman.com/elliptic.htm

Explicit Approaches to Modular Abelian Varieties - William Stein, Ph.D. thesis, Berkeley, 2000.
http://modular.fas.harvard.edu/papers/explicit/

Bibliography for Automorphic and Modular Forms, L-Functions, Representations, and Number Theory - Compiled by Paul Garrett, 1996.
http://www.math.umn.edu/~garrett/m/b/bib.html

Elliptic Curves and Right Triangles - Slides (GIF) of lectures by Karl Rubin at Stanford University.
http://math.stanford.edu/~rubin/lectures/sumo/

Elliptic Curves and Their Applications to Cryptography - Web text by Andreas Enge.
http://www.lix.polytechnique.fr/Labo/Andreas.Enge/buch/buch/buch.html

Elliptic Curves and Elliptic Functions - Introductory notes by Charles Daney.
http://cgd.best.vwh.net/home/flt/flt03.htm

Elliptic Divisibility Sequences - Articles and links, compiled by Graham Everest.
http://www.mth.uea.ac.uk/~h090/EDS.html

Torsion Points on Elliptic Curves - Elementary introduction and brief explanation of some well-known results.
http://mat.uab.cat/~xarles/elliptic.html

Course Notes - Full notes as .dvi, .pdf, and .ps files for all the advanced courses J. S. Milne taught between 1986 and 1999.
http://www.jmilne.org/math/CourseNotes/

ECDL Project - Elliptic Curve Discrete Logarithms Project. They solved ECC2K-108 in April 2000. History and related papers.
http://pauillac.inria.fr/~harley/ecdl/

Elliptic Functions and Elliptic Curves - Lecture notes by Jan Nekovář (PS/PDF).
http://www.math.jussieu.fr/~nekovar/co/ln/el/

Richard Taylor - Publications including the joint paper with Andrew Wiles which completed the proof of Fermat's Last Theorem.
http://www.math.harvard.edu/~rtaylor/