Electronically Available Books and Other Sources (mainly Category Theory)
Not a book in the traditional sense, more like a wiki, containing
much recent category theory not (easily) available elsewhere.
H. Herrlich, G. Strecker: Abstract and Concrete
Categories. John Wiley and Sons, 1990. Contains a lot of
material not available in Mac Lane's book. Indispensable for me.
A. Asperti, G. Longo: Categories, Types and Structures.
MIT Press, 1991. Emphasises the relationship between category theory
and type theory.
C. Wells: Toposes, Triples and Theories. Springer, 1983. A
Basic Concepts of Enriched Category Theory. Cambridge
University Press, 1982. TAC-reprint 2005.
R.M. Burstall: Computational Category Theory.
Prentice-Hall, 1988. (See also here)
Lecture Notes on Category Theory
C. Wells: Introduction to Category Theory. Lecture Notes of
an ESSLLI'99 course.
An Invitation to General Algebra and Universal
Constructions. 1998. An introduction to category theory that
carefully explains many (universal) constructions in algebra and
neighbouring fields. I enjoyed it a lot.
J.M.E. Hyland, G. Winskel: Lecture Notes in Category
Theory. BRICS Lecture Series, 2001.
M. Fokkinga: A Gentle Introduction to Category Theory - the calculational
approach. University of Utrecht, 1992.
Leinster: Category Theory. This page contains an informal
introduction to category theory and, for example, a nice explanation
of the Yoneda Lemma.
van Oosten: Basic Category Theory.
An introduction to Category theory in four easy movements.
Category Theory Lecture Notes. LFCS, Univeristy of
Edinburgh, 2001. If I had the opportunity to teach a first course on
category theory I might choose these as my notes.
Special Topics in Category Theory
Reprints in Theory and Applications of Categories.
Moss: Non-wellfounded Set Theory.
Benabou: Distributors at Work. Course
E. Cheng, A. Lauda: Higher-Dimensional Categories:
an illustrated guide book. Draft, 2004.
Higher Operads, Higher Categories. CUP, 2004.
Category Theory and Categorical Logic.
Course notes, 2004.
Categorical Models of Constructive Logic.
Course notes, 2003.
Fibred Categories a la Benabou.
Course notes, 1999, revised 2003.
Theory and Applications of Categories. Maintained by researchers
and freely available, it is the main journal on category theory and
Logical Methods in Computer Science. Maintained by researchers and
freely available (started in 2005), it may well become the leading
journal in theoretical computer science. Some of the best recent
categorical papers in computer science can be found here.
Archive of ancient mathematics documents. Scanned copies of French
journals and seminaires from 1810 until today. (With papers of, for
example, Chevalley, Ehresmann, Eilenberg, Grothendieck, Moore)
Grothendieck Circle. Website with biographical information about and mathematical work of Alexander Grothendieck.
Related and Unrelated Areas
J. Barwise and S. Feferman: Model-Theoretic
Logics. Springer 1985.
S.N. Burris and H.P. Sankappanavar: A Course in Universal
Algebra. Springer, 1981. A classic text which is still a
J.-Y. Girard, Y. Lafont and P. Taylor: Proofs and
Types. CUP, 1989. Long out of print but luckily available online.
R. Goldblatt: Mathematics of Modality. CSLI, 1993. Contains
many of Goldblatt's groundbraking papers on modal logic.
Algebraic Topology. CUP, 2002. I find it a very readable
introduction emphasising geometric intuition.
R. Sutton, A. Barto: Reinforcement Learning:
An Introduction MIT Press, Cambridge, MA, 1998.
R. Findler, M. Flatt, S. Krishnamurthi: How To Design Programs
MIT Press, Cambridge, MA, 2003.
Online (see also here)
Pennsylvania Library, The Online Books Page
Textbooks in Mathematics