This will be a short review. I picked up Michael Crawford's The Roman Republic at a used bookstore. It was a good basic overview of the functioning of the Roman Republic and how this changed as its history progressed. It's done well enough, I haven't read enough about the Republic to have other specific works to compare to, and felt it was worth taking the time to read.
More generally, I have always found the Roman Republic fascinating, particularly as an example of political decay. It's an excellent example of how an extremely successful society finds itself unable to adapt to its own success and the changing obligations that result from it. Rome simply couldn't deal with the increasing power of its citizens, by the end of the Republic, the state was basically subject to its leading citizens, making the step to monarchy quite small. It's a fascinating topic, and one I plan to write a book about one day.