This book is about orthomorphisms and complete mappings of groups, and
related constructions of orthogonal latin squares. It brings together,
for the first time in book form, many of the results in this area. The
aim of this book is to lay the foundations for a theory of orthomorphism
graphsof groups, and to encourage research in this area. To this end,
many directions for future research are suggested. The material in this
book should be accessible to any graduate student who has taken courses
in algebra (group theory and field theory). It will mainly be useful in
research on combinatorial design theory, group theory and field theory.