The estimation of motion of multi-camera systems is one of the most important tasks in computer vision research. Recently, some issues have been raised about general camera models and multi-camera systems. Using many cameras as a single camera is studied [60], and the epipolar geometry constraints of general camera models is theoretically derived. Methods for calibration, including a self-calibration method for general camera models, are studied [78, 62]. Multi-camera systems are an example of practically implementable general camera models and they are widely used in many applications nowadays because of both the low cost of digital charge-coupled device (CCD) cameras and the high resolution of multiple images from the wide field of views. To our knowledge, no research has been conducted on the relative motion of multi-camera systems with non-overlapping views to obtain a geometrically optimal solution. ¶ In this thesis, we solve the camera motion problem for multi-camera systems by using linear methods and convex optimization techniques, and we make five substantial and original contributions to the field of computer vision. First, we focus on the problem of translational motion of omnidirectional cameras, which are multi-camera systems, and present a constrained minimization method to obtain robust estimation results. Given known rotation, we show that bilinear and trilinear relations can be used to build a system of linear equations, and singular value decomposition (SVD) is used to solve the equations. Second, we present a linear method that estimates the relative motion of generalized cameras, in particular, in the case of non-overlapping views. We also present four types of generalized cameras, which can be solvable using our proposed, modified SVD method. This is the first study finding linear relations for certain types of generalized cameras and performing experiments using our proposed linear method. Third, we present a linear 6-point method (5 points from the same camera and 1 point from another camera) that estimates the relative motion of multi-camera systems, where cameras have no overlapping views. In addition, we discuss the theoretical and geometric analyses of multi-camera systems as well as certain critical configurations where the scale of translation cannot be determined. Fourth, we develop a global solution under an L∞ norm error for the relative motion problem of multi-camera systems using second-order cone programming. Finally, we present a fast searching method to obtain a global solution under an L∞ norm error for the relative motion problem of multi-camera systems, with non-overlapping views, using a branch-and-bound algorithm and linear programming (LP). By testing the feasibility of LP at the earlier stage, we reduced the time of computation of solving LP.¶ We tested our proposed methods by performing experiments with synthetic and real data. The Ladybug2 camera, for example, was used in the experiment on estimation of the translation of omnidirectional cameras and in the estimation of the relative motion of non-overlapping multi-camera systems. These experiments showed that a global solution using L∞ to estimate the relative motion of multi-camera systems could be achieved.