  In this thesis, we study the deformation problem of coisotropic submanifolds
in Jacobi manifolds. In particular we attach two algebraic invariants to any
coisotropic submanifold $S$ in a Jacobi manifold, namely the
$L_\infty[1]$-algebra and the BFV-complex of $S$. Our construction generalizes
and unifies analogous constructions in symplectic, Poisson, and locally
conformal symplectic geometry. As a new special case we also attach an
$L_\infty[1]$-algebra and a BFV-complex to any coisotropic submanifold in a
contact manifold. The $L_\infty[1]$-algebra of $S$ controls the formal
coisotropic deformation problem of $S$, even under Hamiltonian equivalence. The
BFV-complex of $S$ controls the non-formal coisotropic deformation problem of
$S$, even under both Hamiltonian and Jacobi equivalence. In view of these
results, we exhibit, in the contact setting, two examples of coisotropic
submanifolds whose coisotropic deformation problem is obstructed.
