Title: Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
Author: John Derbyshire
Publisher: Joseph Henry Press, 2003
Pages: 361

I've read about Riemann Hypothesis for years, but only as far as the history goes. It wasn't until this book that I began to consider to get my hands dirty and try to understand what the hypothesis really says.

So this book is split into two parts: odd chapters for technical stuff; even chapters for historical background. The idea is that you can skip the odd chapters if you're only interested in the history; or skip the even chapters if you're only interested in the math. As we advance through the book, however, I found this distinction blurred, so you might as well read the whole book.

Overall, this is a very gentle introduction to Riemann Hypothesis. We start with infinite series and prime numbers, then things become more challenging. If you are not a mathematician or you haven't done math in a while but you happened to enjoy math back at school, this book will suit you. But if you want complete history and biography of the people around this hypothesis, I would recommend The Music of The Primes.