  We use nonstandard methods, based on iterated hyperextensions, to develop
applications to Ramsey theory of the theory of monads of ultrafilters. This is
performed by studying in detail arbitrary tensor products of ultrafilters, as
well as by characterizing their combinatorial properties by means of their
monads. This extends to arbitrary sets methods previously used to study
partition regular Diophantine equations on \N. Several applications are
described by means of multiple examples.
