Euclidean space is the space Euclidean geometry uses. In essence, it is described in Euclid's Elements. The Euclidean plane () and three-dimensional space () are part of Euclidean space, which can be generalized to any dimension n (in which case one writes ).
Euclidian space is sometimes called Cartesian space. A few other spaces and mathematical objects that are similar were added later. Euclid based his work Elements on certain axioms. Euclidean space can be described using such axioms.