Here I'll just collect some articles summarizing what I've found out when I've delved into various mathematical topics. There's no real rhyme or reason to the topics except what interested me at the time.
How happy the lot of the Mathematician! He is judged solely by his peers, and the standard is so high that no colleague or rival can ever win a reputation he does not deserve. No cashier writes a letter to the editor complaining about the incomprehensibility of Modern Mathematics and comparing it unfavorably with the good old days when mathematicians were content to paper irregularly shaped rooms and fill bathtubs without closing the waste pipe.
W. H. Auden
The Dyer's HandMathematics is the subject in which we do not know what we are talking about, nor whether what we are saying is true.
Bertrand Russell
Group Theory and Various Important Sets: A brief primer on group theory, leading into a discussion of the defining properties of some well-known and important sets (natural numbers, rationals, reals, and complex numbers).
Mathematics Archives: Lots of links to articles all over the web on various mathematical topics.
Eric Weisstein's World of Mathematics: An excellent reference site (and you can also jump to his excellent reference sites for astronomy, chemistry and physics, and biographies of famous mathematicians and scientists, from here).
Frequently Asked Questions in Mathematics: Another good math info site.