Coordination, consensus, and synchronization are found in diverse natural phenomena and engineering applications. Examples are flocking birds, illuminating fireflies, a school of fish, and distributed control and sensing. The simplest of such problems are set in the Euclidean spaces and the circle. Consensus and Synchronization: From the Euclidean Space and the Circle to Lie Groups moves beyond this domain to the more sophisticated setting of Lie groups with bi-invariant metrics and extends the mathematical theories of consensus and synchronization for generic scenarios. This is relevant to applications such as robotics, autonomous vehicles, and spacecraft.