This book contains the first English translation of the monograph, “The General Theory of Algebraic Equations”, which was published in French in 1779 by Etienne Bézout (1730-1783) under the name, “Théorie Générale des Équations Algébriques“. The book became very popular after its publication. The monograph was translated by Eric Feron, Professor of Aerospace Engineering at Georgia Institute of Technology. The book presents the Bézout approach to the problem of how to solve systems of polynomial equations in several variables and his new notation for the polynomial multiplier, which simplified the problem of variable elimination by reducing it to a system of linear equations. The book describes the major Bézout's result called “the Bézout theorem“, his deep analysis of systems of algebraic equations, his uses of determinants for finding a solution of systems of linear equations, his approach to integration and differentiation of functions, etc. The English translation can be recommended to everyone who is interested in problems of solving systems of polynomial equations and inequalities because it describes this mathematical problem from a historical perspective.