This survey of the most important properties of Chebyshev polynomials encompasses several areas of mathematical analysis: • Interpolation theory • Orthogonal polynomials • Approximation theory • Numerical integration • Numerical analysis • Ergodic theory Starting with some definitions and descriptions of elementary properties, the treatment advances to examinations of extremal properties, the expansion of functions in a series of Chebyshev polynomials, and iterative properties. The final chapter explores selected algebraic and number theoretic properties of the Chebyshev polynomials. For advanced undergraduates and graduate students in mathematics Originally published in 1974, the text was updated in 1990; this reprint of the second edition corrects various errors and features new material.