One of the central questions in analytic number theory is, how are the primes distributed among the set of natural numbers? At first glance, obtaining a satisfactory answer to this question might seem hopeless. For, on the one hand, there exist runs of one million (or more) consecutive composite numbers (Proposition 4.8), while on the other hand, it is believed that there are an infinite number of pairs of prime numbers separated by only one composite number (the twin primes conjecture). In fact, there are rather deep results that provide elegant answers to this question. In this chapter, we will investigate some of these results, and along the way we will become acquainted with some of the basic tools of analytic number theory.