  The purpose of this paper is to establish a connection between various
subjects such as dynamical r-matrices, Lie bialgebroids, and Lagrangian
subalgebras. Our method relies on the theory of Dirac structures developed in
dg-ga/9508013 and dg-ga/9611001. In particular, we give a new method of
classifying dynamical r-matrices of simple Lie algebras $\frak g$, and prove
that dynamical r-matrices are in one-one correspondence with certain Lagrangian
subalgebras of ${\frak g}\oplus \frak g$.
