As an example of general methodology, the evolution of the theory of equations from the Babylonian solution of a quadratic equation to its completion by Galois in 1830 is the focus of these lectures given to undergraduate math majors by Tignol (U. Catholique de Louvain, Belgium) from 1978-89. Includes technical appendices, exercises with selected solutions, and multilingual references from the 16th to 20th centuries. Earlier editions were published in 1988 by Longman and in 1980 in French.