The main subject of this volume is approximation by polynomials, rational functions, splines and operators. There are excursions into the related fields: interpolation, complex variable approximation, wavelets, widths, and functional analysis. Emphasis is on basic results, illustrative examples, rather than on generality or special problems. A graduate student can learn the subject from different chapters of the books; for a researcher they can serve as an introduction; for applied researchers a selection of tools for their endeavours.