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This book deals with mathematically solving the unsteady flame propagation. New original mathematical methods for solving complex non-linear equations and investigating their properties are presented. Pole solutions for flame front propagation are developed. Premixed flames and filtration combustion have remarkable properties: The complex nonlinear integro-differential equations for this problem have exact analytical solutions to describe the motion of poles in a complex plane. Instead of complex equations, a finite set of ordinary differential equations is applied. These solutions help to formulate analytically and numerically the flame front propagation equations.