chapter 1 Definitions -- chapter 2 Basic Properties and Formulae -- chapter 3 The Minimax Property and Its Applications -- chapter 4 Orthogonality and Least-Squares Approximation -- chapter 5 Chebyshev Series -- chapter 6 Chebyshev Interpolation -- chapter 7 Near-Best L∞, L1 and Lp Approximations -- chapter 8 Integration Using Chebyshev Polynomials -- chapter 9 Solution of Integral Equations -- chapter 10 Solution of Ordinary Differential Equations -- chapter 11 Chebyshev and Spectral Methods for Partial Differential Equations -- chapter 12 Conclusion.