  We show that the Nambu-Goto string, and its higher dimensional
generalizations, can be quantized, in the sense of an effective theory, in any
dimension of the target space. The crucial point is to consider expansions
around classical string configurations. We are using tools from perturbative
algebraic quantum field theory, quantum field theory on curved spacetimes, and
the Batalin-Vilkovisky formalism. Our model has some similarities with the
L\"uscher-Weisz string, but we allow for arbitrary classical background string
configurations and keep the diffeomorphism invariance.
