Rotation in two dimensions is introduced in this chapter by reviewing the geometrical and algebraic representation of 2-D rotation. The algebraic representation uses a matrix for the rotation, with a matrix–vector product required to apply the rotation to a vector. The distinction between vector rotation and frame rotation is identified. Rotations in two dimensions are a natural precursor to the 3-D case, though they hide the complexity of the 3-D conical rotation operation. A single parameter is sufficient to represent a 2-D rotation, whereas a minimum of three parameters are required for a 3-D rotation. The properties of the rotation matrix are explored and the relationship between 2-D rotations and complex numbersComplex numbers is examined. The chapter ends with a discussion on the parameter space for 2-D rotations, which is useful for later comparison to the parameter space for the different 3-D rotation parameter spaces.