Computerized devices are becoming smaller and more ubiquitous. Equally importantly, they are becoming more interconnected. A Sensor Network is a model for such interconnected systems. Each sensor device obtains and stores information that is potentially useful to others. The challenge is to efficiently search and deliver the important information to the relevant parties. Given the large number of devices and corresponding quantities of data, this is not easy. Fortunately for us, communication is efficient and fast when addressing nearby devices. This permits us to utilize their relative locations to construct efficient methods.The proximity and location information can be leveraged through the use of geometry. The complexity of a network and data hide simpler geometric structures that are not obvious at first sight. The objective in this dissertation is to identify such concealed structures that can be useful and can be computed in the network. An abstract structure or Abstraction helps us to understand and represent the network and data in more convenient ways. This approach is useful in managing the data in the network, as well as in managing the network itself. Its utility is demonstrated through accompanying algorithms in each part of the dissertation.