Genstat 5 Release 3 is a version of the statistical system developed by practising statisticians at Rothamsted Experimental Station. It provides statistical summary, analysis, data-handling, and graphics for interactive or batch users, and includes a customizable menu-based interface. Genstat is used worldwide on personal computers, workstations, and mainframe computers by statisticians, research workers, and students in all fields of application of statistics. Release 3 contains many new facilities: the analysis of ordered categorical data: generalized additive models; combination of information in multi-stratum experimental designs; extensions to the REML (residual maximum-likelihood) algorithm for testing fixed effects and to cater for correlation strucgures between random effects; estimation of paramenters of statistical distributions; further probability functions; simplified data input; and many more extensions, in high-resolution graphics, for calculations, and for manipulation. The manual has been rewritten for this release, including new chapters on Basic Statistics and REML, with extensive examples and illustrations. The text is suitable for users of Genstat 5 i.e. statis