The Euler Characteristic is a topological invariant that provides a way to classify surfaces based on their shape. It is calculated using the formula \chi = V - E + F , where V represents the number of vertices, E is the number of edges, and F is the number of faces in a polyhedron. For example, a sphere has an Euler characteristic of 2, while a torus has an Euler characteristic of 0. This concept, named after the mathematician Leonhard Euler, helps in understanding the properties of different geometric structures. The Euler characteristic is particularly useful in fields like algebraic topology and graph theory, where it aids in distinguishing between different types of surfaces and shapes.