I've already consulted four different textbooks on the history of (ancient) philisophy (the ones by Russell, Giovanni Reale/Dario Antiseri, Sir Anthony Kenny and the one I use in high school), as well as Russell's The problems of philosophy and some articles on SEP.
Nonetheless, I still don't completely understand Plato's theory of Forms. I have a feel that all of those books require some prior knowledge about the topic and so leave out lots of details.
This is, roughly, what I don't understand:
I don't get what an idea/form actually is. I know that an idea can be attributed to a class of particulars which share some properties, but what is the idea of that?
What are the arguments in favour of the existence of ideas?
Which philosophical problems does the theory solve?
Are there modern philosophers who support the theory?
Can you suggest a book, or a series of books, which answers these questions in a rigorously logical, complete and "self-contained" way?