Comparing maps is an important issue in environmental research. Reasons for comparing maps may be: (i) the different socio-economic scenarios on which they are based, (ii) detection of temporal changes, (iii) calibration/validation of land-use models, (iv) hot-spot detection, (v) their use in uncertainty analysis, and (vi) their origin in different methodologies/models. This report addresses the problem of quantifying subsequent map similarities and dissimilarities.Our main focus is on maps denoted as 'categorical' or 'nominal'. A number of the five map- comparison techniques are described. These techniques differ in mathematical approach (no math, 'cell by cell', two types of 'fuzzy' and 'single-map statistics') and apply to different types of maps (nominal, ordinal, ratio and interval scale). Special attention is given to the comparison of maps through fuzzy-set calculation rules. The rationale is that fuzzy-set map comparison is very close to human judgement, as shown in an Internet experiment.The MAP COMPARISON KIT (MCK) software plays a major role in the report. MCK, a software package for 'state-of-the-art' map comparison, contains all the examples used in this report. The software, developed by order of the Netherlands Environmental Assessment Agency, was fully designed by the Research Institute for Knowledge Systems. The software will be made publicly available on the RIVM website early 2004 (www.rivm.nl).