This monograph presents a unified theory of nuclear structure and nuclear reactions in the language of quantum electrodynamics, Feynman diagrams. It describes how two-nucleon transfer reaction processes can be used as a quantitative tool to interpret experimental findings with the help of computer codes and nuclear field theory. Making use of Cooper pair transfer processes, the theory is applied to the study of pair correlations in both stable and unstable exotic nuclei. Special attention is given to unstable, exotic halo systems, which lie at the forefront of the nuclear physics research being carried out at major laboratories around the world. This volume is distinctive in dealing in both nuclear structure and reactions and benefits from comparing the nuclear field theory with experimental observables, making it a valuable resource for incoming and experienced researchers who are working in nuclear pairing and using transfer reactions to probe them.