1. Functional integrals In quantum theory.- §1. Gaussian functional integrals for systems of non-interacting particles.- §2. Methods of functional integration for interacting particles.- 2. Superfluid Bose systems.- §1. Perturbation theory for superfluid Bose systems.- §2. The effective action functional for superfluid systems.- §3. Quantum vortices in superfluid systems.- 3. Superfluid Fermi systems.- §1. Perturbation theory for superfluid Fermi systems.- §2. Collective excitations in superfluid Fermi systems.- 4. Interaction of radiation with matter. The linear theory.- § 1. Coherent and thermal radiation.- §2. The two-level system in an external field.- 5. Superradiant phase transitions.- §1. The static field in the single-centre model of the interaction of matterwith single-mode radiation.- §2. The static field in the multi-centre model of the interaction of matter withsingle-mode radiation.- §3. Other models and a discussion of the results.- 6. Superradiant coherent impulses.- § 1. Non-linear interaction of light with matter.- §2. The dynamics of the single-centre model of the interaction of lightwith matter.- §3. The dynamics of the single-mode multi-centre model of the interaction oflight with matter.- Concluding Remarks.