This text contains some facts, ideas, and techniques that can help or motivate the reader to read books and papers on various classes of functions on the disk and the circle. The reader will find several well known, fundamental theorems as well as a number of the author's results, and new proofs or extensions of known results. Most of assertions are proved, although sometimes in a rather concise way. A number of assertions are named by Exercise, while certain assertions are collected in Miscellaneous or Remarks: most of them can be treated by the reader as exercises.
The reader is assumed to have good foundation in Lebesgue integration, complex analysis, functional analysis, and Fourier series, which means in particular that he/she had a good training through these areas. It is of some importance that the reader can accept the following:
Throughout this text, constants are often given without computing their exact values. In the course of a proof, the value of a constant С may change from one occurrence to the next. Thus, the inequality 2C <= С is true even if С > 0.