This article introduces the group of conformal isometries in flat space(-time) with an arbitrary number of dimensions and arbitrary signature, with emphasis on the embedding space formalism. The embedding space formalism relates conformal isometries in N dimensions to ordinary isometries in N+2 dimensions. When N≥ 3, this gives the full group of conformal isometries. This article also introduces the concept of conformal completion (also called conformal compactification) and describes the conformal completion of Minkowski spacetime, including its topology and how it relates to conformal isometries.
