Book Recommendation for Integer partitions and $q$ series I have been studying number theory for a little while now, and I would like to learn about integer partitions and $q$ series, but I have never studied anything in the field of combinatorics, so are there any prerequisites or things I should be familiar with before I try to study the latter?

George Andrews has contributed greatly to the study of integer partitions. (The link with his name will take you to his webpage listing publications, some of which are accessible as pdf documents.) Also see, e.g., his classic text The Theory of Partitions and the more recent Integer Partitions.
You can pretty much "jump right in" with the following, though their breadth of coverage may be more than you care to explore (in which case, they each have fine sections on the topics of interest to you, with ample references for more in depth study of each topic):
Two books I highly recommend are 
Concrete Mathematics by Graham, Knuth, and Patashnik.
Combinatorics: Topics, Techniques, and Algorithms by Peter J. Cameron. See his associated site for the text.
