Indexation of wages, pensions and tax scales to allow for inflation requires a reliable measure of the rate of inflation. In Australia the Consumer Price Index (C.P.I.) has been the basis of all official indexation. This paper examines both theoretical and practical problems involved in constructing a C.P.I. and the Australian C.P.I. in particular. Alternative indices of the rate of inflation such as a Wholesale Price Index and an Implicit Price Deflator, are also discussed.