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.