ANALYSIS I, 4TH EDITION: 1 (Texts and Reading in Mathematics) Hardcover

part one of a two-volume introduction to real analysis. The emphasis is on rigour and on foundations. The material starts at the very beginning - the construction of the number systems and set theory - then goes on to the basics of analysis, through to power series, variable calculus and Fourier analysis, and finally to the Lebesgue integral.