This chapter presents Euler’s rotation theorem and Euler’s rotation formulaEuler’s rotation formula. The theorem provides the key parameters required to define a rotation, i.e. the axis of rotation and the angle of rotation. Euler’s rotation formula then provides the details for the calculations necessary to perform a rotation on a vector given the axis of rotation and the angle of rotation. The modern version of the formula is derived using matrix/vector operations and is equivalent to Euler’s original form. Importantly, Euler’s formula provides a way in which the rotation matrix is obtained using the axis and angle of rotation.