Given a graph $G$, one can compute the eigenvalues of its adjacency matrix $A_G$. Remarkably, these eigenvalues can tell us quite a bit about $G$. More generally, spectral graph theory consists of taking a graph $G$, associating to it a matrix $M_G$, and then using algebraic properties of $M_G$ to recover combinatorial information about $G$. This talk is the first in a series of introductory talks to the subject of spectral graph theory. In particular, we'll be discussing the adjacency matrix and the information encoded by its eigenvalues.