Latin squares: Introduction and some methods for construction.

The presentation is concerned with Latin squares, their connection with algebraic structures such as groups, loops, and quasigroups, and methods for constructing Latin squares of large orders. Some basic facts about Latin squares and their properties are mentioned. A new family of Latin squares of prime orders specified with the use of permutations is introduced. Finally, Latin squares over Abelian groups defined with the use of special families of functions (called proper families) are considered.