Excellent read for a Mathematics Undergraduate,
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This review is from: Riemann's Zeta Function (Dover Books on Mathematics) (Paperback)
I bought this book to help with my Mathematics Masters Project on the Riemann Hypothesis and the Riemann Zeta Function.
I find the book very useful as it is detailed and clear, and fills in many of the 'missing' steps in Bernhard Riemann's 1859 paper. It has all the topics you would expect to see, and has a particularly good chapter on the analytic continuation of the zeta function, proof of the functional equation and how the zeros of the zeta function link to the primes.
A must read for any undergraduate Mathematics student looking to further their understanding. And it's much cheaper than the alternatives!