Check out the Wikipedia entry on Combinatorics. It will include a good distillation of the field(s), since "Combinatorics" is huge and encompasses seemingly unrelated "subfields". The entry will also point to some good references and links. See also Gentle Introduction to Ramsey's Theory , and once you've done that, review Ramsey's Theory, more technical. See also this earlier post: What is Ramsey's Theory? What is its own importance in maths?
As Alex suggests, one of the nice things about combinatorics is that it doesn't require much in the way of prerequisites: you can "dig in" and run with it. You can study sub-topics within Combinatorics that are fairly well-contained, like graph theory, and doing so doesn't require knowledge of every thing that counts as "Combinatorics." See also this earlier post: What is Combinatorics?.
One of my favorite texts in Combinatorics is Peter Cameron's text Combinatorics. But if you search Math.SE using the tags "reference-request" and "Combinatorics", you'll find a host of previously recommended texts.