欧几里得几何指按照欧几里得的《几何原本》构造的几何学。

欧几里得几何有时就指二维平面上的几何，即平面几何。本文主要描述平面几何。三维空间的欧几里得几何通常叫做立体几何。高维的情形请参看欧几里得空间。

数学上，欧几里得几何是指二维平面和三维空间中的几何，基于点线面假设。数学家也用这一术语表示具有相似性质的高维几何。

其中公设五又称之为平行公设（Parallel Axiom），叙述比较复杂，这个公设衍生出「三角形内角和等于一百八十度」的定理。在高斯（F. Gauss, 1777年—1855年）的时代，公设五就备受质疑，俄罗斯数学家罗巴切夫斯基（Nikolay Ivanovitch Lobachevski）、匈牙利人波约（Bolyai）阐明第五公设只是公理系统的一种可能选择，并非必然的几何真理，也就是「三角形内角和不一定等于一百八十度」，从而发现非欧几里得的几何学，即「非欧几何」（non-Euclidean geometry）。

Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated by earlier mathematicians, Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system. The Elements begins with plane geometry, still taught in secondary school as the first axiomatic system and the first examples of formal proof. It goes on to the solid geometry of three dimensions. Much of the Elements states results of what are now called algebra and number theory, explained in geometrical language.