A lattice L in a semisimple Lie group G is a discrete subgroup
of G for which the quotient L\G has finite volume. One may
construct lattices using number theory and such lattices are
said to be ""arithmetic"". Lattices that cannot be constructed
in this way are called ""non-arithmetic"" are hard to find.
In this talk we focus on the case where G=3DSU(n,1). The first
non-arithmetic lattices in SU(2,1) were constructed by
Mostow in 1980. Subsequently Deligne and Mostow found a
family of non-arithmetic lattices in SU(2,1) and a single
example in SU(3,1).

[Invited by R. Kellerhals and J. Paupert]