THEORETICAL DEVELOPMENT AND APPLICATIONS OF RHOTRICES. In this dissertation, the algebra and analysis of rhotrix, a new paradigm of matrix theory, whose goal is central on representation of arrays of numbers in Mathematical rhomboid form, are reviewed. The generalization and axiomatization of the space of real rhotrices are presented. The development of the rhotrix exponent rule and their applications to the study of some special series and polynomial equations over rhotrices are also studied. The classifications of rhotrices into some abstract structures and topological spaces are proposed. Further openings of this relatively new area of research in the study of multidisciplinary aspect of Mathematical Sciences such as Graph theory, Optimization and Computer Science, which may be applied in solving real life problems are suggested for future work. This book therefore, is particularly suitable for both undergraduate and postgraduate students studying Algebra, Analysis, Topology, Number Theory, Graph Theory, Optimization theory and Computer Science, who are interested in getting exposed to a new direction in Mathematical discipline called 'Rhotrix theory and Applications'.