  We study Hamiltonian spaces associated with pairs (E,A), where E is a Courant
algebroid and A\subset E is a Dirac structure. These spaces are defined in
terms of morphisms of Courant algebroids with suitable compatibility
conditions. Several of their properties are discussed, including a reduction
procedure. This set-up encompasses familiar moment map theories, such as
group-valued moment maps, and it provides an intrinsic approach from which
different geometrical descriptions of moment maps can be naturally derived. As
an application, we discuss the relationship between quasi-Poisson and
presymplectic groupoids.
