One of the central themes of modern number theory is the intimate connection between various arithmetic and analytic objects; these connections lie at the heart of many of recent breakthroughs and current programs of research, including the modularity theorem, the Sato-Tate theorem, the Riemann hypothesis, the Birch and Swinnerton-Dyer conjecture, and the Langlands program. Having said that, number theory is, after all, the study of numbers, thus our starting point is the ring Z, its field of fractions Q, and the various completions and algebraic extensions of Q. This means we will begin with some standard topics in algebraic number theory, including: Dedekind domains, decomposition of prime ideals, local fields, ramification, the discriminant and different, ideal class groups, and Dirichlet's unit theorem. We will spend most of the first half of the semester on these topics, and then move on to some closely related analytic topics, including zeta functions and L-functions, the prime number theorem, primes in arithmetic progressions, the analytic class number formula, and the Chebotarev density theorem. I also plan to cover at least the statement of the main theorems of local and global class field theory, as well as a preliminary discussion of Artin representations, Hecke characters, and their associated L-functions.