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 operators on Hilbert spaces, which are fundamental in quantum physics. They help in understanding the mathematical foundations of quantum mechanics and have applications in various areas of mathematics and physics.