  A well known result of Drinfeld classifies Poisson Lie groups $(H,\Pi)$ in
terms of Lie algebraic data in the form of Manin triples
$(\mathfrak{d},\mathfrak{g},\mathfrak{h})$; he also classified compatible
Poisson structures on $H$-homogeneous spaces $H/K$ in terms of Lagrangian
subalgebras $\mathfrak{l}\subset\mathfrak{d}$ with
$\mathfrak{l}\cap\mathfrak{h}=\mathfrak{k}=\mathrm{Lie}(K)$. Using the language
of Courant algebroids and groupoids, Li-Bland and Meinrenken formalized the
notion of \emph{Dirac Lie groups} and classified them in terms of so-called
"$H$-equivariant Dirac Manin triples" $(\mathfrak{d}, \mathfrak{g},
\mathfrak{h})_\beta$; this generalizes the first result of Drinfeld, as each
Poisson Lie group gives a unique Dirac Lie group structure. In this thesis, we
consider a notion of homogeneous space for Dirac Lie groups, and classify them
in terms of $K$-invariant coisotropic subalgebras
$\mathfrak{c}\subset\mathfrak{d}$, with $\mathfrak{c}\cap\mathfrak{h} =
\mathfrak{k}$. The relation between Poisson and Dirac morphisms makes
Drinfeld's second result a special case of this classification.
