This monograph deals with the description and design of digital images. Regarding digital images as special input/output relations in our previous book with LNCIS series, the description problem of digital images is transformed into the realization problem of digital images. From the data in digital images, mathematical models will be constructed. Then new systems which describe faithfully any digital images provide new results and their extensions which design digital images. As concerned with mathematical models for digital images, this monograph introduces 2-Commutative Linear Representation Systems for two-dimensional images and 3-Commutative Linear Representation Systems for three-dimensional images. This monograph is intended for researchers and graduate students who specialized in image processing and system theory.