The Anger camera has been used for the last quarter century in many areas of science to image gamma radiation. Some typical applications include medicine, where functionality of organs are studied in vivo, and industrial inspection of fuel rods for nuclear reactors. The standard Anger geometry includes a large scintillation crystal, light guide, photomultiplier array, and analog processing electronics. Even the most modern gamma cameras built today still use the standard Anger design. The work presented here describes an alternative to the standard gamma-camera design that is flexible enough to be used in a wide variety of applications. Especially in single-photon emmission computed tomography (SPECT) applications, the new design has the potential to be more efficient than the standard design. The new design is modular, that is, several small, separate units comprise a system. Each unit consists of a small gamma camera that is optically and electronically independent from other units. The units, called "modular cameras," can be configured around the region of interest so as to provide the maximum amount of information for reconstruction algorithms or direct information to the operator. The theoretical and experimental investigation of this report focuses on the design and construction of the modular cameras. Each modular camera is, in esscence, a small Anger camera. Components of each module include a scintillation crystal, a light guide, and an array of four photomultiplier tubes. Instead of an analog processing network, each module utilizes fast digital circuitry which includes direct analog-to-digital conversion of the photomultiplier signals, a lookup table which maps detector responses to position estimates of the scintillation flashes in the crystal, and an image memory which accumulates the position estimates and forms an image of the radiation incident on the faceplate of the camera. The digital electronics are necessary because analog techniques fail to give satisfactory estimates of scintillation position when the flashes occur near the sides of the crystal. The contents of the lookup table are determined from the statistical properties of the detected signals as a function of scintillation position. Experiments are described in which "best" estimates of position are found by processing data collected from an array of point-source positions in contact with the crystal. Alternative methods for construction of the lookup table are also discussed, which involve computer generation of the estimates. Both maximum-likelihood and mimimum-mean-square-error estimation rules are used, and the results are compared. A mathematical bound on the performance of the estimators is calculated assuming Poisson statistics for the detection process. The bound, which is a Cramer-Rao lower bound, is used to compare module geometries before lookup tables are constructed. A one-dimensional module, which accumulates information along one axis of the faceplate, is designed first. The one-dimensional module provides proof-of-principle evidence for the estimation techniques and is used to determine critical parameters for modular-camera design. The results of the experiments with the one-dimensional camera are extended to two-dimensional designs, which yield position estimates along both axes of the camera faceplate. Several two-dimensional cameras are tested, and an optimum geometry is constructed and tested for spatial resolution and bias of the estimators.