This text is a single variable real analysis text, designed for the one-year course at the junior, senior, or beginning graduate level. It provides a rigorous and comprehensive treatment of the theoretical concepts of analysis. The book contains most of the topics covered in a text of this nature, but it also includes many topics not normally encountered in comparable texts. These include the Riemann-Stieltjes integral, the Lebesgue integral, Fourier series, the Weiestrass approximation theorem, and an introduction to normal linear spaces.