Kinematic couplings are used when two rigid bodies need to be repeatedly and accurately positioned with respect to each other. They allow for sub-micron positioning repeatability by suppressing play and reducing strains in the bodies. Typical applications are lens mounts, work piece mounts and docking interfaces for astrophysics, semiconductor and metrology applications. This thesis generalizes the well-known concept of two-body kinematic couplings to three-body kinematic mounts. The goal of the thesis is: To pave the way for high precision assembly using kinematic mounts by providing an exhaustive catalogue of all twobody and three-body kinematic mounts and to test key configurations experimentally. The main contributions of this thesis are: - State of the art survey of essential knowledge in the field of kinematic couplings. - Rigorous problem statement for the design of two-body and three-body kinematic mounts. - Rigorous limitation of the scope of research to three-body kinematic mounts whose contact points lie exclusively on three convergent orthogonal lines and whose constraint lines are parallel to these lines. - An exhaustive catalogue of three-body kinematic mounts consisting of seven configurations in 3D and nine configurations in 2D. - An exhaustive set of four conditions satisfied by three-body 3-dimensional kinematic mounts. - An exhaustive set of seven conditions satisfied by three-body 2-dimensional kinematic mounts. - Realization of a two-body kinematic mount and a three-body kinematic mount in metal, and precise measurement of their positioning accuracy on a 3D coordinate measurement machine at the Swiss Federal Institute of Metrology. Positioning error of 0.2 microns and 5 microradian achieved with two-body kinematic mounts. Positioning error of 1 micron and 50 microradian achieved with three-body kinematic mounts. - Realization of three-body kinematic mounts in Silicon by Deep Reactive Ion Etching processes (DRIE) and experimental measurement of their positioning error. - Physical implementation of nesting forces and assembly methods allowing for the physical construction of kinematic mounts. - Physical realizations in robotics, optics and aerospace using our new kinematic mounts.