We present Newton's main ideas for the formulation of classical mechanics as given in the Principia. Then we discuss Ernst Mach's criticisms of Newtonian mechanics as contained in his book The Science of Mechanics. We analyze the influence of Mach's ideas in the teaching of classical mechanics considering five representative textbooks: those of Kittel, Knight and Ruderman; Marion and Thornton; Symon; Feynman, Leighton and Sands; and Goldstein. We conclude that the influence of Mach's ideas has been very great, being incorporated in the textbooks, although not always with the deserved acknowledgment. © 2001 Kluwer Academic Publishers.101-2137144Blackmore, J.T., (1972) Ernst Mach: His Work, Life and Influence, , University of California Press, Berkeley(1970) Ernst Mach: Physicist and Philosopher, , Cohen, R. S. & Seeger, R. J. (eds): Reidel, DordrechtFeynman, R.P., Leighton, R.B., Sands, M., (1963) The Feynman Lectures on Physics, Volume 1: Mainly Mechanics, Radiation, and Heat, 1. , Addison-Wesley, ReadingGoldstein, H., (1980) Classical Mechanics, 2nd Edition, , Addison-Wesley, ReadingKittel, C., Knight, W.D., Ruderman, M.A., (1965) Mechanics, Volume 1: Berkeley Physics Course, 1. , McGraw-Hill, New YorkMach, E., (1960) The Science of Mechanics - A Critical and Historical Account of Its Development, , Open Court, La SalleMarion, J.B., Thornton, S.T., (1995) Classical Dynamics of Particles and Systems, 4th Edition, , Saunders College Publishing, Fort WorthMatthews, M.R., (1994) Science Teaching: The Role of History and Philosophy of Science, , Routledge, New YorkNewton, I., (1934) Mathematical Principles of Natural Philosophy, , Cajori edition, University of California Press, BerkeleySymon, K.R., (1971) Mechanics, 3rd Edition, , Addison-Wesley, ReadingZylbersztajn, A., Newton's absolute space, Mach's principle and the possible reality of fictitious forces (1994) European Journal of Physics, 15, pp. 1-8