  This is an introduction to graph theory, from a geometric viewpoint. A finite
graph $X$ is described by its adjacency matrix $d\in M_N(0,1)$, which can be
thought of as a kind of discrete Laplacian, and we first discuss the basics of
graph theory, by using $d$ and linear algebra tools. Then we discuss the
computation of the classical and quantum symmetry groups $G(X)\subset G^+(X)$,
which must leave invariant the eigenspaces of $d$. Finally, we discuss similar
questions for the quantum graphs, with these being again described by certain
matrices $d\in M_N(\mathbb C)$, but in a more twisted way.
