Benoit Mandelbrot was a graduate of Ecole Polytechnique and the University of Paris, and received a masters degree in aeronautics at the California Institute of Technology. In 1958 he joined the IBM Thomas J. Research Council, where he was an IBM Fellow, taking periodic leaves to teach at Harvard University as Visiting Professor of Economics, and, later, of applied mathematics. He also taught at Yale, the University of Paris-Sud, M.I.T., and the Albert Einstein College of Medicine. He was a Fellow of the Guggenheim Foundation, Trumbull Lecturer at Yale, Samuel Wilks Lecturer at Princeton, and Abraham Wald Lecturer at Columbia. It was as Lecturer at Collège de France that he gave in 1973 and 1974 the lessons which eventually were developed into the present essay; he discovered the Mandelbrot set in 1980 through his use of the computing power available to him at IBM.