Spin is a fundamental degree of freedom of matter and radiation.In quantum theory, spin is represented by Pauli matrices.Then the various algebraic properties of Pauli matricesare studied as properties of matrix algebra. What has beenshown in this article is that Pauli matrices are a representationof Clifford algebra of spin and hence all the propertiesof Pauli matrices follow from the underlying algebra. Cliffordalgebraic approach provides a geometrical and henceintuitive way to understand quantum theory of spin, and isa natural formalism to study spin. Clifford algebraic formalismhas lot of applications in every field where spin plays animportant role.