Some preliminary reading for the RH Saga

If you are planning to follow the RH Saga course notes, and you need to brush up on complex analysis, here are some really nice lecture notes by Dan Romik. The chapters are brief, and chapter 15 covers all the basic properties of the Riemann zeta function.

These lectures notes have also been developed into a longer book, called Topics in Complex Analysis, which covers much more (like modular forms and sphere packing) and is available for free from the publisher website.

Finally, if you want to start exploring the primes and their connection with the Riemann spectrum, I recommend the book by Mazur and Stein called Prime numbers and the Riemann Hypothesis.