In the previous lectures, we have defined the Shannon Capacity of a graph, Θ(G). This lecture is concerned with the Shannon Capacity of the disjoint union G +H of two graphs G and H. The union of two graphs is, informally, what you get when you just place one graph next to the other. In 1956, Shannon conjectured [1] that Θ(G + H) = Θ(G) + Θ(H). As we will see, this is a very natural conjecture ...