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

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/

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

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/

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

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

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

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

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

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/

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

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

Moonshine Bibliography
- Books and papers relating to the Conway-Norton-Thompson Moonshine conjecture, proved by Richard Borcherds.
- http://cicma.concordia.ca/faculty/cummins/moonshine.refs.html

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

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

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

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

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

Monstrous Moonshine
- the surprising and mysterious connections between the monster (and also other finite sporadic simple groups) and modular functions.
- http://cicma.concordia.ca/faculty/cummins/moonshine.html

A Proof of the Full Shimura-Taniyama-Weil Conjecture
- PDF-format article by Henri Darmon on the completion of the proof by Wiles, Breuil, Conrad, Diamond and Taylor.
- 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 Handout
- Syllabus and detailed reading list by Miles Reid, University of Warwick.
- http://www.maths.warwick.ac.uk/~miles/MA426/

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

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

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

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

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

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

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/

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

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