球面几何学是在二维的球面表面上的几何学，也是非欧几何的一个例子。

在平面几何 中，基本的观念是点和线。在球面上，点的观念和定义依旧不变，但线不再是“直线”，而是两点之间最短的距离，称为测地线。在球面上，最短线是大圆的弧，所以平面几何中的线在球面几何中被大圆所取代。同样的，在球面几何中的角被定义在两个大圆之间。结果是球面三角学和平常的三角学有诸多不同之处。例如：球面三角形的内角和大于180°。

对比于通过一个点至少有两条平行线，甚至无穷多条平行线的双曲面几何学，通过特定的点没有平行线的球面几何学是椭圆几何学中最简单的模式。

Spherical geometry is the geometry of the two-dimensional surface of a sphere. It is an example of a geometry that is not Euclidean. Two practical applications of the principles of spherical geometry are navigation and astronomy.

In plane geometry, the basic concepts are points and (straight) lines. On a sphere, points are defined in the usual sense. The equivalents of lines are not defined in the usual sense of "straight line" in Euclidean geometry, but in the sense of "the shortest paths between points", which are called geodesics. On a sphere, the geodesics are the great circles; other geometric concepts are defined as in plane geometry, but with straight lines replaced by great circles. Thus, in spherical geometry, angles are defined between great circles, resulting in a spherical trigonometry that differs from ordinary trigonometry in many respects; for example, the sum of the interior angles of a triangle exceeds 180 degrees.