A classical optimization problem in graph theory is the maximum flow problem. Given a weighted directed graph, what is the maximum amount of flow that can be pushed between two fixed vertices s and t? The max-flow-min-cut theorem states that the maximum flow value is equal to the minimum value of a cut. Interestingly, this theorem can be stated using the language of sheaf cohomology. This talk will introduce cellular sheaves and build up to the restatement of the theorem