This report is an aid to demographers and population experts to analyze censuses that became universal operations providing crucial information on national populations. However, the reliability and completeness of census results remain uneven and in several countries only one census has been implemented. This is the main reason why the census-based methods of estimating population size and particularly the methods for adjusting incomplete and deficient census data and extrapolating census results presented in Manual I, which has been compiled in the 1950s, remain relevant. The techniques to use incomplete and deficient data for estimating other demographic parameters from censuses and other sources are presented in Manuals II and IV.