Situations arising from the fields of transportation, water resources, manufacturing and many others give rise to network flow models. A flow network is a collection of nodes and arcs. Each arc passes from one node to another and carries a commodity called flow. A requirement is that flow be conserved at each node. The optimization problem is to find the flow in each arc that minimizes the total cost of the flow in the network. This topic has three aspects: modeling real problems as networks, the theory associated with network optimization, and algorithms implementing the theory. The course covers the broad range of network flow problems, but stresses the pure and generalized, single commodity, minimum cost network flow problem.