We use monopole Floer homology for sutured manifolds to construct invariants of
unoriented Legendrian knots in a contact 3–manifold. These invariants assign to a
knot K ⊂ Y elements of the monopole knot homology KHM(−Y,K), and they
strongly resemble the knot Floer homology invariants of Lisca, Ozsváth, Stipsicz,
and Szabó. We prove several vanishing results, investigate their behavior under
contact surgeries, and use this to construct many examples of nonloose knots in
overtwisted 3–manifolds. We also show that these invariants are functorial with
respect to Lagrangian concordance.