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This book presents a modified method, based on multidimensional residue theory, for the elimination of unknowns from a system of nonlinear algebraic equations. An algorithm is given for constructing the resultant of the system, and a computer implementation making use of formula manipulation software is carried out. Programmes in MAPLE are available. The algorithms and programmes are then applied to questions from the theory of chemical kinetics, such as the search for all stationary solutions of kinetic equations and the construction of kinetic polynomials. The subject of this book is closely connected with a wide range of current problems in the analysis of nonlinear systems. Audience: This volume will be of interest to graduate students and researchers whose work involves multidimensional theory of residues, mathematical kinetics, computer algebra, and symbolic computation.