There is no one good book defining republican government which in any case has to be understood in a variety of forms and within different historical contexts. Some books however are essential: Aristotle’s Politics, Cicero’s De Republica, Livy's History and Machiavelli’s Discourses on Livy. In the American tradition I would study Jefferson and Calhoun and perhaps John Adams. There are several central themes essential to the republican tradition and I shall mention two or three.
First is the emphasis on law and tradition taking precedence over both the will of the sovereign (whether king or democratic majority) and raison d’état. Then there is the acknowledgment of the valid powers of the constituent social authorities of family, clan, region, church sometimes simplistically summed up as subsidiarity. Finally I would point to institutional strategies to avoid tyranny especially the tyranny of the majority that AT so feared but also the lesser tyranny of Louis Napoleon in which AT initially acquiesced. We discussed some of these themes in connection with the Politics.
(I have edited the post for the typing errors.)