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In this article the author focuses on the problem of maximizing the flow through a network in which the nodes and arcs have limited capacity. Each arc has a positive rational capacity representing the maximum amount of flow that may pass across it, and each node has a positive rational capacity representing the maximum amount of flow that may enter or leave it. The author also describes the linear program that maximizes flow through the network and illustrates how cut sets are used to solve the problem. He also use illustrations and diagrams to emphasize his point. The author remarks that the problem of maximizing flow, through a network with node and arc capacities can be formulated as a linear program. The linear formulation has been presented and the relations between variables has been explained by the author. The author has also described the algorithm for finding a maximum flow pattern that starts out with a flow of zero on all arcs. The algorithm attempts to find a chain from source to sink with unused capacity on all of its arcs and nodes.