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 the structure $g$. 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 $g$. in this talk we discuss some of the more common applications of spectral graph theory, as well as a very simple proof of the sensitivity conjecture due to huang.