  Constructive and nonconstructive techniques are employed to enumerate Latin
squares and related objects. It is established that there are (i)
2036029552582883134196099 main classes of Latin squares of order 11; (ii)
6108088657705958932053657 isomorphism classes of one-factorizations of
$K_{11,11}$; (iii) 12216177315369229261482540 isotopy classes of Latin squares
of order 11; (iv) 1478157455158044452849321016 isomorphism classes of loops of
order 11; and (v) 19464657391668924966791023043937578299025 isomorphism classes
of quasigroups of order 11. The enumeration is constructive for the 1151666641
main classes with an autoparatopy group of order at least 3.
