A Prime Case of Chaos: Article from Volume 4 of What's Happening in the Mathematical Sciences by Barry Cipra, describing conjectural links between the Riemann zeta function and chaotic quantum-mechanical systems.
Not Always Buried Deep: Notes on Analytic and Combinatorial Number Theory, originally written for the 2003 Ross Summer Mathematics Program, by Paul Pollack.
Riemann's Paper: "Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse" and in translation.