The purpose of this paper is to present an idea of geometry described by set theory. This method can describe the axioms of the different geometric representations of space. The axioms of Euclid will be described through straight, segment or sphere subsets, for example the axiom of parallels will be described through a straight set and the definition of the acute angle. The axioms of algebra will be described in the same way using subsets of space with original properties. This description by set theory makes it possible to make a theoretical link between geometry and algebra, and to make a practical link between formulas from different mathematical universes such as trigonometry, algebra and geometry. Apart from the description of axioms, this paper makes it possible to reformulate and explain the meaning of theorems (trigonometric formula, Euler formula, etc.) in an original way, in order to find coherent and efficient methods of describing space.