These notes were developed to teach a two semester sequence in graph theory at Simon Fraser where we generally use West's book: Introduction to Graph Theory. The first semester covers the first five sections (up to Directed Graphs) and the second the remainder. Although my arrangement is roughly similar to that of West, my notes differ in a number of ways. For one, I am less algorithmic in my treatment, and there is no discussion of complexity. Another notable difference is that instead of introducing many concepts and a great lot of notation early on, my introduction is slower, with more time is spent on a concept when we arrive there.