What is Geometry?

Geometry is a branch of mathematics that focuses on questions of size, shape, the properties of space, and relative position of figures. Mathematicians who work in the geometry field are referred to as geometers.
In several early cultures, geometry arose as a practical approach for dealing with volumes, areas, and lengths. While geometry has changed significantly over the years, there are several concepts that are more or less basic to geometry. These concepts include points, surfaces, angles, curves, and lines.
Geometry is applied in many fields, including physics, architecture, art, as well as other branches of mathematics. Modern geometry has several subfields:
Euclidean geometry—this is geometry in its classical sense. It has applications in crystallography, computer science, and various branches of contemporary mathematics.
Differential geometry—this subfield uses techniques of linear algebra and calculus to study problems in geometry.
Topology –This subfield deals with the geometric object’s properties that are unaffected by continuous mappings.
Convex geometry –examines convex shapes in the space of Euclidean and it’s more abstract analogs.
Algebraic geometry– studies geometry using multivariate polynomials or other algebraic methods.
Discrete geometry—it mainly focuses on relative position questions of geometric objects, such as lines, points, and circles.
References
http://www.corestandards.org/Math/Content/HSG/introduction/
https://www.cut-the-knot.org/WhatIs/WhatIsGeometry.shtml

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