I was recently introduced to dimensional analysis and I wanted good references for learning the ideas behind it and representation of the natural world. I'm a grad student in biology. I don't have much of a physics background.
This is a great summary of dimensional analysis written by Ain Sonin, a former professor of mechanical engineering at MIT. It's only ~50 pages, and most of it should be accessible to you. Though some examples may draw on parts of physics you're not familiar with, it is very well-written and should clarify the subject greatly.