Catalogue of Algebraic Systems
The catalogue was compiled by John Pedersen. John moved and I inherited
it. The catalogue is still quite incomplete. However, following it I have
listed some additional links where you might find what you are looking
for.  W. Edwin Clark ,
Additional Links
Since the above catalogue was compiled much more information on algebraic
matters has appeared on the web. Below are links to some of these webpages.
I have just begun collecting them . If you know of others that would be
appropriate to add please let me know. As of now they are listed in no
particular order. Organization may come later. W. Edwin Clark eclark@math.usf.edu

Geoffrey Dixon's Technical Pages on Division
Algebras (especially, Quaternions and Octonions), Lie Algebras, Lie Groups,
Spinors and Lattices

To see how much we have to add, browse: 1991
Mathematics Subject Classification

Atlas of Finite
Group Representations. by Robert Wilson, et al.

The Number of
Groups of Order n where n is at most 1000 and other Combinatorial Data.
by Gordon Royle

GAP , Groups, Algorithms
and Programming, is a FREE system for computational discrete algebra with
particular emphasis on computational group theory. GAP includes various
databases including all groups of order up to 1,000, excluding 512 and
768.

Perhaps the most general algebraic structure (outside of category theory)
is the universal algebra. For a brief introduction and some history
see: Hermann
Grassmann and the Prehistory of Universal Algebra by Desmond FearnleySander

Three element groupoids.
by Stanley Burris

Three element groupoids
with unary operation. by Stanley Burris

Dave
Rusin's Algebraic Areas of Mathematics from his Mathematical Atlas This
itself contains quite a catalogue of algebraic systems.

Eric Weisstein's Encyclopedia
of Mathematics Many algebraic systems are described here.

Modern
Algebra Topics from the Math Forum's Internet Mathematics Library.

Algebraic Systems
This is essentially a textbook on algebraic systems put together by
Christer Blomqvist. Compared to Weisstein's site above, this is more of
a tutorial. So take a look if you want more discussion. It is written in
English, but includes A very brief English to Swedish dictionary .

Groupoid
Homepage These groupoids are small categories where all morphism are
isomorphisms and are not to be confused with the other groupoids which
are sets with a single binary operation. See Ronald Brown's discussion
of groupoids in
the categorical sense.

Applied and
Computational Category Theory This includes a brief history and description
of category theory.

Higher Dimensional
Group Theory By Ronald Brown.

E. Lee Lady's Notes This
includes Notes on Homological Algegra, A Course in Abstract Algebra, and
Torsion Free Modules over Dedekind Domains.

The
Net Advance of Physics This is a list of links similar to the one you
are in now of topics of an algebraic naturemany, but not all, related
to physics. The list is compiled and managed by Norman Redington.

Zero Divisor
Structure in Real Algebras by Steve Finch.

Sketch of the
history of hypercomplex numbers Note that hypercomplex numbers are
better known as associative algebras .

Logic and Philosophy
of Mathematics Section of Stanford's Encyclopedia of Philosophy This
includes entries for many interesting topics including category theory
and the
home page for the axiom of choice .

Semigroup Mailing
List A mailing list to go to for technical questions about semigroups.

Small Semigroups Reference to a paper
on the number of semigroups of orders up to 8 by S. Satoh, et al.

Abstract Algebra On Line
This site contains many of the definitions and theorems from abstract algebra.
It is intended for undergraduate students taking an abstract algebra class
at the junior/senior level, as well as for students taking their first
graduate algebra course. It is based on the following books: Abstract
Algebra Second Edition, by John A. Beachy and William D. Blair, and
Abstract Algebra II, by John A. Beachy.

The Rubik's cube group
( which has order 43252003274489856000) from the homepage of W.
D. Joyner which links to Joyner's Permutation
Puzzle Page and other algebraic matters of interest.

Rubik's Cube
Page A LOT of Rubik's cube information by Michael Reid.;

Rubik's Cube Solutions by Josef
"Gloom" Jelinek and Dr. Hana M. Bizek.

Maple
Worksheets for Abstract Algebra This is a collection of Maple worksheets
by Fr Mike May, S.J. The worksheets are mainly concerned with field theoryGalois
theory, finite fields, etc.

Diamond Theory by Steven H.
Cullinane. See also The
Diamond 16 Puzzle also by Steven Cullinane. The puzzle displays the
affine group on the 4space over GF(2) as generated by row/column/quadrant
permutations of a 4x4 array.

Exploring Abstract Algebra with
Mathematica by Al Hibbard and Ken Levasseur. This is a collection
of Mathematica packages that enable one to work with concepts from abstract
algebra (including groups, rings, fields, and morphisms).