  In this paper, we study deformations of coisotropic submanifolds in a
symplectic manifold. First we derive the equation that governs $C^\infty$
deformations of coisotropic submanifolds and define the corresponding
$C^\infty$-moduli space of coisotropic submanifolds modulo the Hamiltonian
isotopies. This is a non-commutative and non-linear generalization of the
well-known description of the local deformation space of Lagrangian
submanifolds as the set of graphs of {\it closed} one forms in the
Darboux-Weinstein chart of a given Lagrangian submanifold. We then introduce
the notion of {\it strong homotopy Lie algebroid} (or {\it
$L_\infty$-algebroid}) and associate a canonical isomorphism class of strong
homotopy Lie algebroids to each pre-symplectic manifold $(Y,\omega)$ and
identify the formal deformation space of coisotropic embeddings into a
symplectic manifold in terms of this strong homotopy Lie algebroid. The formal
moduli space then is provided by the gauge equivalence classes of solutions of
a version of the {\it Maurer-Cartan equation} (or the {\it master equation}) of
the strong homotopy Lie algebroid, and plays the role of the classical part of
the moduli space of quantum deformation space of coisotropic $A$-branes. We
provide a criterion for the unobstructedness of the deformation problem and
analyze a family of examples that illustrates that this deformation problem is
obstructed in general and heavily depends on the geometry and dynamics of the
null foliation.

Symplectic Geometry;High Energy Physics - Theory;Quantum Algebra