In this chapter, we will introduce the Bloch sphere to which a 2D complex space of a single qubit is mapped. The Bloch sphere is embedded in the real 3D space. As a result, the manipulation of a qubit by a quantum gate is equivalent to a rotation on the Bloch sphere. We will show the rotation matrix of an arbitrary quantum gate and its decomposition. Then we will discuss Pauli matrices and their properties. Pauli matrices are the generators of rotations. Understanding the properties of the Pauli matrices helps us derive many important equations. Finally, we will discuss the universal sets of quantum gates which can be used to implement all quantum gates.