Geometry is a branch of mathematics concerned with the properties and relationships of points, lines, shapes, sizes, angles, and the spatial characteristics of objects. It studies figures and the space they occupy, including their distance, shape, size, and relative positions. Originally developed to model the physical world, geometry covers both two-dimensional shapes like lines, circles, triangles, and polygons, as well as three- dimensional solids like cubes, spheres, prisms, and cylinders. It has applications in many fields including art, architecture, physics, and more advanced areas of mathematics such as algebraic geometry and general relativity. There are several types of geometry, including:

• Euclidean geometry, which deals with flat spaces and classical shapes,
• Non-Euclidean geometries, which explore curved spaces and surfaces,
• Analytical geometry, which represents geometric figures using algebraic equations.

Geometry also studies concepts like points (which have no size, only position), lines (one-dimensional), planes (two-dimensional), and solids (three-dimensional). It helps understand patterns and measures in the world around us. The field dates back to ancient Greece, with Euclid regarded as the "Father of Geometry" through his foundational work in the subject. Modern geometry has expanded vastly, now including the study of manifolds — spaces that locally resemble ordinary Euclidean space but can have complex global structures. In summary, geometry provides the language and tools to analyze and describe the form, structure, and space of physical and abstract objects in a rigorous mathematical way.