  We introduce geometric quantization in the setting of shifted symplectic
structures. We define Lagrangian fibrations and prequantizations of shifted
symplectic stacks and their geometric quantization. In addition, we study many
examples including symplectic groupoids, Hamiltonian spaces and moduli spaces
of flat connections. In the case of Hamiltonian spaces we prove a derived
analog of the "quantization commutes with reduction" principle.
