**Geometry** is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.[1] A mathematician who works in the field of geometry is called a geometer.

## Important concepts in geometry

- Axioms
- Points
- Lines
- Planes
- Angles
- Curves
- Surfaces
- Manifolds
- Length, area, and volume
- Metrics and measures

- Congruence and similarity
- Compass and straightedge constructions
- Dimension
- Symmetry

## Contemporary geometry

- Euclidean geometry
- Differential geometry
- Non-Euclidean geometry

- Topology
- Algebraic geometry
- Complex geometry
- Discrete geometry
- Computational geometry
- Geometric group theory
- Convex geometry