This book demonstrates the newly developed Elementary Operations Algorithm (EOA). This is a systematic method for constructing a range of state-space realizations for 2-D systems. The key achievements of the monograph are as follows: - It provides a research-level introduction to the general area and undertakes a comparative critical review of previous approaches. - It gives a thorough coverage of the theoretical basis of the EOA algorithm. - It demonstrates the effectiveness of the EOA algorithm, for example, through the use of algebraic symbolic computing (using MAPLE), as well as by comparing this method with common alternatives.