In Ancient Greece, Euclid gave a proof that there are infinitely many primes. Since then, mathematicians have been interested in studying the distributions of these primes. In 1837, Dirichlet provided a theorem stating that there are infinitely many primes congruent to a modulo b when $gcd(a,b) = 1$. Dirichlet's proof of this remarkable fact can be thought of as the beginnings of analytic number theory. This talk aims to introduce objects such as L-functions and Maass forms, and the ideas relating these objects to number theoretical problems.