A C*-algebra is a type of mathematical structure used in functional analysis, a branch of mathematics. It consists of a set of complex-valued functions that can be added together and multiplied, along with a special operation called the *involution*. C*-algebras are equipped with a norm, which allows for the measurement of size or distance, and they satisfy specific properties that make them useful in various areas of mathematics and physics. These algebras are particularly important in the study of quantum mechanics and operator theory, where they help describe the behavior of quantum systems. The concept was developed in the 1930s by mathematicians like John von Neumann and David Hilbert, and it has since become a fundamental tool in both pure and applied mathematics.