Part I Introduction.- Latin Squares Based on Groups.- When is a Latin Square Based on a Group?.- Part II Admissable Groups.- The Existence Problem for Complete Mappings: The Hall-Paige Conjecture.- Some Classes of Admissible Groups.- The Groups GL(
n
,
q
), SL(
n
,
q
), PGL(
n
,
q
), and PSL(
n
,
q
).- Minimal Counterexamples to the Hall-Paige Conjecture.- A Proof of the Hall-Paige Conjecture.- Part III Orthomorphism Graphs of Groups.- Orthomorphism Graphs of Groups.- Elementary Abelian Groups I.- Elementary Abelian Groups II.- Extensions of Orthomorphism Graphs.- ω(
G
) for Some Classes of Nonabelian Groups.- Groups of Small Order.- Part IV Additional Topics.- Projective Planes from Complete Sets of Orthomorphisms.- Related Topics.- Problems.- References.- Index.