The goal of this text is to provide a collection of results which generalize classical real analysis. Topics discussed include density, approximate continuity and approximate derivatives in detail, culminating with the Denjoy-Saks-Young Theorem. The authors also present an interesting example due to Ruziewicz on an infinite number of functions with the same derivative but the difference of any two is not a constant and Sierpinski's theorem on the extension of approximate continuity to nonmeasurable functions. There is also a chapter on monotonic functions and one dealing with the...