Nonlinear minimization problems -- Minimization with linear operators -- Nonlinear operators in LP, 1<p?? -- L? Minimization problems for elliptic operators -- L1 minimization in one and several variables -- Sets of uniqueness in L? minimization problems -- Bang-Bang optimal controls -- A general theorem of Kuhn-Tucker type -- Stable and unstable elastica equilibrium and the problem of minimum curvature -- Approximation by extremals of nonlinear differential expressions in one variable and quadratic forms in several variables -- The trigonometric and algebraic favard problem -- Minimization and interpolation at integer points of the real axis -- The Landau problem and Kolmogorov’s theorem -- Perfect interpolating splines on compact intervals -- A pólya algorithm for the favard solution, N-width characterizations and Whitney type theorems -- Application of the Riesz-Fredholm-Schauder theory to spline functions -- Epilogue.