Title page
I. Introduction
II. Purely Periodic Functiona and Their Fourier Series
General Orthogonal Systems
Fourier constants with respect to a normal orthogonal system. Their minimal property. Bessel's formula and Bessel's inequality
Fourier series of periodic functions
Operations with Fourier series
Two fundamental theorems. The Uniqueness theorem and Parseval's equation
Lebesgue's proof of the uniqueness theorem
The multiplication theorem
Summability of the Fourier series. Fejer's theorem
Weierstrass' theorem
Two remarks
III. The theory of Almost Periodic Functions
The main problem of the theory
Translation numbers
Definition of almost periodicity
Two simple properties of almost periodic functions
The invariance of almost periodicity under simple operations of calculation
The mean value theorem
The concept of the Fourier series of an almost periodic function. Derivation of Parseval's equation
Calculations with Fourier Series
The uniqueness theorem. Its equivalence with Parseval's equation
The multiplication theorem
Introductory remarka to the proof of the two fundamental theorems
Preliminaries for the proof of the uniqueness theorem
Proof of the uniqueness theorem
The fundamental theorem
An important example
Appendix I . Generalizations of Almost Periodic Functions
Appendix II . Almost Periodic Functions of a Complex Variable
Bibliography