As an introductory explanation of the theory of Fourier's series, this clear, detailed text is outstanding. The third revised edition, which is here reprinted unabridged, contains tests for uniform convergence of series, a thorough treatment of term-by-term integration and the second theorem of mean value, enlarged sets of examples on infinite series and integrals, and a section dealing with the Riemann Lebeague theorem and its consequences. An appendix compares the Lebeague definite integral with the classical Riemann integral.