Noncommutative geometry is a branch of mathematics that extends traditional geometry by allowing the coordinates of space to be noncommutative. This means that the order in which you multiply these coordinates matters, similar to how matrix multiplication works. It provides a framework for studying spaces where classical geometric concepts break down, such as in quantum physics. Developed by mathematician Alain Connes, noncommutative geometry connects various fields, including functional analysis and theoretical physics. It offers tools to analyze spaces that are not well-defined in the classical sense, enabling new insights into the structure of space-time and the behavior of particles at the quantum level.