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Approximation theory is an established field, and my aim is to teach you some of its most important ideas and results, centered on classical topics related to polynomials and rational functions. The style of this book, however, is quite different from what you will find elsewhere. Everything is illustrated computationally with the help of the Cheb fun software package in Matlab, from Chebyshev interpolants to Lebesgue constants, from the Weierstrass approximation theorem to the Remez algorithm. Everything is practical and fast, so we will routinely compute polynomial interpolants or Gauss quadrature weights for tens of thousands of points.