An in-depth look at real analysis and its applications, including an introduction to waveletanalysis, a popular topic in "applied real analysis". This text makes a very natural connection between the classic pure analysis and the applied topics, including measure theory, Lebesgue Integral,harmonic analysis and wavelet theory with many associated applications.*The text is relatively elementary at the start, but the level of difficulty steadily increases*The book contains many clear, detailed examples, case studies and exercises*Many real world applications relating to measure theory and pure analysis*Introduction to wavelet analysis