The course will provide important theoretical techniques relevant to Quantum Technologies. Part I - Basic Photonic Quantum Optics: Field quantisation, single-mode fields and quantum states, beam splitters and interferometers, non-classical light and its generation. Part II - Interacting Systems of Cold Atoms: Microscopic description of interacting cold atoms from first principles (pseudopotentials for two-particle scattering; second-quantised field operator Hamiltonian), introduction of approximate methods to treat cold atoms (Bogliubov theory; classical fields and Gross-Pitaevskii equation) and cold atoms in optical lattices (Hubbard models and corresponding phase diagrams).