If you haven't studied it before, start with A.Liddle's 'Introduction to modern cosmology', or B.Ryden's 'Introduction to cosmology'. Both require little more than being comfortable with secondary school/first semester university physics and calculus. The former is more concise and clearly structured, the latter includes more information.
Once you've worked through either (or both) of these, you can look at the further reading sections for more recommendations (e.g. Peebles). However, it must be said that pretty much anything more advanced will require being conversant with general relativity, with all the background that requires.