What do we mean by inequality comparisons? If the rich just get richer and the poor get poorer, the answer might seem easy. But what if the income distribution changes in a complicated way? Can we use mathematical or statistical techniques to simplify the comparison problem in a way that has economic meaning? What does it mean to measure inequality? Is it similar to National Income? Or price index? Is it enough just to work out the Gini coefficient? This book tackles these questions and examines the underlying principles of inequality measurement and its relation to welfare economics, distributional analysis, and information theory. The book covers modern theoretical developments in inequality analysis, as well as showing how the way we think about inequality today has been shaped by classic contributions in economics and related disciplines. Formal results and detailed literature discussion are provided in two appendices. The principal points are illustrated in the main text, using examples from US and UK data, as well as other data sources, and associated web materials provide hands-on learning.