Includes bibliographical references (p. [151]-159) and index.

Implicit functions -- An informal version of the implicit function theorem -- The implicit function theorem paradigm -- Historical introduction -- Newton -- Lagrange -- Cauchy -- The inductive proof of the implicit function theorem -- The classical approach to the implicit function theorem -- The contraction mapping fixed point principle -- The rank theorem and the decomposition theorem -- A counterexample -- Ordinary differential equations -- Numerical homotopy methods -- Equivalent definitions of a smooth surface -- Smoothness of the distance function -- The Weierstrass preparation theorem -- Implicit function theorems without differentiability -- An inverse function theorem for continuous mappings -- Some singular cases of the implicit function theorem -- Analytic implicit function theorems -- Hadamard""s global inverse function theorem -- The implicit function theorem via the Newton-Raphson method -- the Nash-Moser implicit function theor .