A C*-algebra is a type of mathematical structure used in functional analysis and quantum mechanics. It consists of a set of complex-valued functions that can be added together and multiplied, along with a special operation called the *adjoint*. This structure must satisfy certain properties, such as being closed under limits and having a norm that relates to the adjoint operation. C*-algebras are important because they provide a framework for studying linear operators on Hilbert spaces, which are essential in quantum physics. They also connect to other areas of mathematics, such as representation theory and topology, making them a vital tool in both pure and applied mathematics.