An endomorphism is a type of mathematical function that maps a set or structure to itself. In simpler terms, it takes an object from a specific space and transforms it into another object within the same space, while preserving the structure of that space. This concept is commonly used in various fields of mathematics, including algebra and geometry. For example, in the context of vector spaces, an endomorphism can be represented as a matrix that operates on vectors within that space. The result of this operation is still a vector in the same space, making it a crucial concept in understanding transformations and symmetries in mathematics, particularly in relation to linear algebra and group theory.