Abstract: Noncommutative geometry was discovered by Alain Connes in the early 80's. In short, noncommutative geometry is based on a duality between the categories of algebra and geometry. A noncommutative space is thought of as the dual object to a noncommutative algebra. In my talk, I will discuss the ideas of noncommutative geometry and concepts in the category of geometry which admit noncommutative versions, and of course examples.