Though of course we could divide this up even further, I'll argue that the basic ways of philosophizing/theorizing/thinking about democracy fall into three major categories:
1. The Ghost of Plato: Democracy stultifies and corrupts us. It exacerbates our biases and our worst behaviors. Here I include not only Plato and others historically concerned about mob rule, but also the recent empirical work on voter ignorance and irrationality, the new epistocratic critiques, and empirical work on democratic realism and the ideological innocence of voters
2. The Spirit of Equality: Democracy is fundamentally a mechanism by which we realize an ideal of equality. It makes us all equals and allows us to see each other eye-to-eye. Here I include Rousseau and de Tocqueville, Dewey, contemporary neorepublicans, the deliberative democrats.
3. The Shadow of the Market: Democracy is a form of trade and exchange by other means. Democracy enables people to get what they want and lead their live as they choose. But just as markets can fail, so the democratic market can fail. Here I include many of the early American and British pro-democracy thinkers, the authors of the Federalists Papers, the public choice tradition, and your sixth grade civics teacher.
While I'll cover roughly 2500 years in this one book, a good third of the book or more will be about works written in the past 75 years. Frankly, most of the best work on democracy was written recently, because it was only recently that we started having good social science to help inform and set parameters for our normative theorizing.