This is a book for experts. After you learn the basics of Lebesgue integration (some algebra is very useful, too), you can open your eyes to how vast is the reach and breadth of the modern generalizations of integration theory. Here, the authors make use of the more elegant and powerful presentations of the integral: the main development is along the lines of Daniell, and after the treatment is extended to topological groups via the Haar integral. Applications in operator theory and a discussion about a interesting analogy between the integral as an algebraic entity and the trace of operators in von Neumann algebras, and how it can be used to construct a "non-commutative" theory of integration. This set of topics is almost impossible to find at this depth, even more in a single book.