Despite the fact that the discipline of economic inequality measurement is thriving in the last twenty or so years (may be thirty something if you count from Atkinson (1970) paper), the textbook format publications of the general character are rare; I can only think of Lambert (2002) as another major source. Amartya Sen is a Nobel prize winner in the area of inequality, poverty and famines; and James Foster who wrote an extensive commentary featured in this second edition of the original Sen's lectures is arguably the most often cited author in inequality and poverty measurement due to his principal contributions on the classes of decomposable measures and poverty orderings.
It should be noted that Sen is kinda difficult reading; his language is a little bit archaic, and not very typical for the modern highly mathematized economic publications (don't worry, you'll see enough abstract algebra once you start going into the details of the derivation of the properties of inequality/poverty indices...)
I don't think that the other review gives anything close to the real merit of this book, as it seems to be written by an information econometrician rather than somebody doing substantive distribution research. I would comment that generalized entropy measures are important, if not central, in the inequality measurement due to their nice properties, but are not the only measures possible. The authors rather wanted to give a big picture, and, as I said, you can get all sorts of details in the article publications they refer to.