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We study the stability and capacity problems in regular wireless networks. In the first part of the paper, we provide a general approach to characterizing the capacity region of arbitrary networks, find an outer bound to the capacity region in terms of the transport capacity, and discuss connections between the capacity formulation and the stability of node buffers. In the second part of the paper, we obtain closed-form expressions for the capacity of Manhattan (two-dimensional grid) and ring networks (circular array of nodes). We also find the optimal (i.e., capacity-achieving) medium access and routing policies. Our objective in analyzing regular networks is to provide insights and design guidelines for general networks. The knowledge of the exact capacity enables us to quantify the loss incurred by suboptimal protocols such as slotted ALOHA medium access and random-walk-based routing. Optimal connectivity and the effects of link fading on network capacity are also investigated.