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The subject of multidimensional systems, as originally conceived, is concerned with a mathematical framework for tackling a broad range of paradigms whose analysis or synthesis require the use of functions and polynomials in either several complex or real variables. Its applications, which may range from the processing of spatial and temporal signals of diverse physical origin to the design of linear continuous-discrete multidimensional control systems, are already plentiful. This paper aims to promote interaction between a broad spectrum of scientists and engineers through clear exposition and interpretation of fundamentals, albeit a daunting task, so that complex theoretical results become useful to practitioners in distinct but related disciplines. The expanding arena of theory and applications of the original aims and scopes attest to the importance and vitality of the subject-matter.