The Harmonized Index of Consumer Prices (HICP) is the single most important indicator of inflation used by the European Central Bank. Sections 2 to 4 of the paper look at the theory of inflation indexes that could be used as target indexes of inflation. A Consumer Price Index (CPI) emerges as perhaps the most useful target index. Four different approaches to index number theory are reviewed and the 'best' index number formula from each perspective is determined. Section 6 looks at the methodology of the HICP in the light of the previous sections. Section 7 looks at some of the difficult measurement problems that must be addressed in a CPI or an HICP. These problems include the treatment of quality change, substitution or representativity bias, chained versus fixed base indexes, the choice of formula at the lowest level of aggregation and the treatment of owner occupied housing and seasonal commodities.