Geometry is the branch of mathematics concerned with the properties and relationships of points, lines, surfaces, solids, and angles. Geometry may be thought of as the science of space. Indeed, just as arithmetic is used to deal with experiences involving the counting process, so geometry is used to describe and relate experiences that involve space.

The fundamental ideas of geometry are suggested by everyday experiences. Thus, the experience of where an object is leads to the idea of an exact, fixed location. This is the intuitive idea to which the term "point" refers. Many physical objects suggest the idea of a point. Examples include the corner of a block, the tip of a pencil, or a dot on a sheet of paper. Such things are called models or representations or pictures of points, although they show only approximately the idea in mind. Similarly, the set of points suggested by a tightly stretched string, the edge of a desk, or a flagpole is called a line segment. The physical objects that suggest line segments are called models, or representations, of segments. If a segment is extended indefinitely in one direction, it is called a ray, and if extended indefinitely in both directions, it is called a line. Similarly, the word "plane" is used to describe a flat surface like a floor, desktop, or chalkboard, but it is imagined as extending indefinitely in all directions. This means that a plane has no edges just as a line has no ends.

The study of geometric figures that lie in one plane is often called plane geometry. The study of figures not all in one plane may be called solid geometry. Frequently, however, no distinction is made, and plane geometry and solid geometry are studied together as parts of the same course.