Dirichlet's Theorem and L-functions

Dirichlet's Theorem states that given any two relatively prime positive integers a, m, there are infinitely-many primes p in the arithmetic progression a + mk where k is any nonnegative integer. This thesis will start with an introduction to the foundations of algebra, number theory, and analysis, and will build on these concepts to introduce the advanced concepts used in the proof of Dirichlet's Theorem.