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Abstract Genstat 5 Release 3 is the latest version of the well-known 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 mulgti-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 rewirtten for this release, including new chapters on Basic Statistics and REML, with extensive examples and illustrations.