Thus there are very many important inequalities.This book is not intended to be a compendium of these; instead, it provides an introduction to a selection of inequalities, not including any of those mentioned above. The inequalities that we consider have a common theme; they relate to problems in real analysis, and more particularly to problems in real analysis. Incidentally, they include many of the inequalities considered in the fascinating and ground-breaking book Inequalities,by Hardy, Littlewood and Polya, originally published in 1934.