Non-commutative geometry is a branch of mathematics that extends traditional geometry by allowing the coordinates of space to be non-commutative. In simple terms, this means that the order in which you measure or combine certain quantities matters, similar to how multiplication of matrices works. This approach helps to describe spaces that are more complex than those found in classical geometry. Developed by mathematician Alain Connes, non-commutative geometry has applications in various fields, including quantum physics and string theory. It provides a framework for understanding the geometry of spaces where conventional notions of distance and angle may not apply, offering new insights into the structure of the universe.