The study of self-adjoint subalgebras of \({\mathcal {B}}(H)\) is an essential tool in the study of linear operators on Hilbert space. However the subject of C*-algebras has developed into a separate discipline of its own, with a more algebraic character. In this chapter, we develop their basic properties culminating in the GNS construction, showing that every abstract C*-algebra can be faithfully represented on a Hilbert space. Then we establish the spectral theorem for normal operators. After that, we take a look at a variety of examples. Special attention is paid to C*-algebras of groups and the property of amenability.