In this chapter the most important properties of the operator of singular integration $$(S_{\Gamma\varphi})(t)=\frac{1}{\pi i}\underset{\Gamma}{\int}\frac{\varphi(\tau )}{\tau -t}d\tau$$ as well as various theorems on the boundedness of this operator will be explained. Moreover, fundamental properties of the operator adjoint to SΓ are proved and the connection of the operator SΓ with the operator of multiplication with a continuous function is studied.