The theory of transformations concerns itself with changes in the coordinates and shapes of objects upon the action of geometrical operations, dynamical boosts, or other operators. This chapter deals with linear transformations, using examples from both plane geometry and relativistic dynamics. It shows how transformation techniques play an important role in image processing, and in generating iterative constructs. The chapter describes both the problems and their solutions in the language of matrices. It explores inversion about the origin, reflection about the coordinate axes, rotation, and scaling are operations that can be represented by a multiplicative matrix, and therefore the composite operation of acting successively on a figure by one or more of these operations can be described by a product of matrices. Matrices are denoted by boldface type and matrix multiplication by an asterisk. The chapter discusses the matrix representation for geometrical and velocity boosts transformations.