  We develop the deformation theory of symplectic foliations, i.e. regular
foliations equipped with a leafwise symplectic form. The main result of this
paper is that each symplectic foliation has an attached $L_\infty$-algebra
controlling its deformation problem. Indeed, viewing symplectic foliations as
regular Poisson structures, we establish a one-to-one correspondence between
the small deformations of a given symplectic foliation and the Maurer-Cartan
elements of the associated $L_\infty$-algebra. Using this, we show that
infinitesimal deformations of symplectic foliations can be obstructed. Further,
we relate symplectic foliations with foliations on one side and with
(arbitrary) Poisson structures on the other, showing that obstructed
infinitesimal deformations of the former may give rise to unobstructed
infinitesimal deformations of the latter.
