The thesis presents new results on multi-agent formation control, focusing on the distributed stabilization control of rigid formation shapes. It analyzes a range of current research problems such as problems concerning the equilibrium and stability of formation control systems, or the problem of cooperative coordination control when agents have general dynamical models, and discusses practical considerations arising during the implementation of established formation control algorithms.  In addition, the thesis presents models of increasing complexity, from single integrator models, to double integrator models, to agents modeled by nonlinear kinematic and dynamic equations, including the familiar unicycle model and nonlinear system equations with drift terms. Presenting the fruits of a close collaboration between several top control groups at leading universities including Yale University, Groningen University, Purdue University and Gwangju Institute of Science and Technology (GIST), the thesis spans various research areas, including robustness issues in formations, quantization-based coordination, exponential stability in formation systems, and cooperative coordination of networked heterogeneous systems.