Why this book, is so immensely good, and (even more importantly)
Why you should read it
Plato's Republic is, any many ways, the exact opposite of contemporary political science - This is what makes it such a substantial work for politically interested people. In contrast with just about every other book on political science, The Republic is written in a captivating way. It discusses politics and political change - but it does not just tell you what needs to be changed, but also how and why - two questions frequently ignored otherwise.
Plato's radical way of observing politics is a substantial challenge to the modern reader. It provokes you to to think critically about politics, society, and the way in which we study them - the primary objective of any good book.
The best example of a thought-provoking issue is how readers today react to Plato's critique of democracy. The fun part is that everybody assumes that they have an answer of why democracy is the best form of government. By raising fundamental questions, both political and philosophical, the reader is forced to reconsider (or at least rethink) their views. Plato teaches us to have a closer look at our biases about democracy - we are forced to "defend" our form of government, based on reason in stead of emotion or authority
Another thing you can't help but admire with Plato is his way of manipulating his discussion partners. Closely related to other, less amicable debate techniques, but also with truly good speech and deduction techniques, Plato invariably puts his point across nicely.
In any case; If you have any interest in politics at all, go read this book!