A *(Learning Lounge) course about *(Category Theory).

The basics:

<ul>
  <li>A category is a thing with objects and arrows (called _(morphism)s) that lead between the objects. The arrows have heads and tails. They are abstract in the sense that they can represent anything with complex structure or even no structure at all. Many categories are different, and there are types of categories.</li>
  <li>All categories follow some basic rules. The differences otherwise 
  can be enormous, though:
    <ul>
      <li>For every object there is an identity arrow over that object that 
      just leads from that object to that object. There may be other 
      identities over that object, but one is distinctly <em>the 
      identity</em>.
      <li>If one arrow leads to an object from which another arrow leads, 
      then those arrows can compose. All such arrows compose, but what you 
      can say about the resulting arrow differs from category to category.
      <li>Some arrows are the reverse or inverse of others.
    </ul>
  </li>
  <li>There are some basic examples of categories: one is Set, whose 
  objects are sets and whose arrows are (total) functions between sets. 
  The category Set's natural composition is therefore function 
  composition.</li>
  <li>The general benefit of the category abstraction is that it allows 
  you to take a kind of entity and use the natural similarities 
  (morphisms) between them to describe a certain structure that they 
  have. You would say that the category of your objects is isomorphic 
  (has the same shape as) to some more familiar computational metaphor, 
  and then you can deal with those abstract things in the same way as 
  the simpler ones.</li>
</ul>

Short introduction:
<ul>
  <li>_("Category Theory entry"
  | http://plato.stanford.edu/entries/category-theory/) on the Stanford 
  Encyclopedia of Philosophy.</li>
  <li>_("Category Theory entry"
  | http://mathworld.wolfram.com/CategoryTheory.html) on Eric Weisstein's 
  World of Mathematics by Eric W. Weisstein.</li>
  <li>_("A Categorical Manifesto"
  | http://www-cse.ucsd.edu/users/goguen/ps/manif.ps.gz) by Joseph Goguen.
  <em>Note:</em> this paper tells you Why Category Theory Matters, but 
  it will not be of much help in actually learning category theory -
  perhaps will help you to relate categorical concepts to more concrete 
  issues in mathematics and computer science.</li>
  <li>_("A gentle introduction to category theory"
  | http://wwwhome.cs.utwente.nl/~fokkinga/mmf92b.html) by Maarten M.
  Fokkinga. This is definitely a better text, with some examples. It 
  does not covers triples (_(aka) _(monad)s, see _(Monads 101)), but covers 
  categories, functors, naturality, adjointness, duality, 
  initiality/finality, products/sums, limits/colimits.</li>
  <li>You may also integrate with the challenging tutorial written by 
  _(David Madore): _("An  introduction to the theory of categories"
  | http://www.eleves.ens.fr:8080/home/madore/math/#didactic). The 
  tutorial is 50 pages long, dense with concepts and using examples 
  mainly from ... er ... algebraic geometry? You may also find some 
  stuff on categorical logic, but only in French. See under 
  mathematics/dissertations and mathematics/thoughts.</li>
</ul>

Online textbooks:
<ul>
  <li>Andrea Asperti and Giuseppe Longo, _("Categories, Types and 
  Structures. An introduction to Category Theory for the working 
  computer scientist"
  | http://www.di.ens.fr/users/longo/download.html). 
  Available online only because it is out of print. A heavyweight 
  tome.</li>
  <li>_("A Categorical Primer" | http://citeseer.nj.nec.com/487012.html).</li>
</ul>

Offline textbooks:
<ul>
  <li><u>Conceptual mathematics: a first introduction to categories</u>, 
  F. William Lawvere, Stephen H. Schanuel.  Cambridge, New York: 
  Cambridge University Press, 1997. This book is very pedagogical and 
  doesn't require any mathematical bewanderedness above highschool 
  algebra.</li>
  <li><u>Practical Foundations of Mathematics</u>, Paul Taylor. 
  Cambridge university Press, 1999. This offline (and online) book is 
  about most <em>everything</em>: Having topos theory and constructivist 
  logic as its main thread, it encompasses roughly the courses
  _(Basic Logic 101), _(Basic Computer Science), _(Category Theory 101),
  algebra and more. _("The homepage for the book"
  | http://www.dcs.qmul.ac.uk/~pt/Practical_Foundations/), with its online
  version. Alas, the online HTML version has only a limited number of formulas
  and no graphics, therefore you definitely want the printed one.</li>
  <li><u>Categories for the Working Mathematician</u>, Saunders Mac 
  Lane. Springer-Verlag, New York-Berlin, 1971. This is <em>the</em> 
  book on category theory from the mathematician who actually introduced 
  categories and functors. Highly Challenging, and not much related with 
  computer science for what I (_(schizophonic)) know.</li>
</ul>