Fourier transform spectroscopy (FTS) is one of the most important tools in the study of shallow level donors and acceptors in semiconductors. When combined with a two-step photothermal ionization process detected photoconductively, FTS allows measurement of optical transitions of donor-bound electrons (and acceptor-bound holes) in ultra-pure germanium samples with impurity concentrations <109 cm−3 (i.e. one electrically active impurity in 4×1013 host atoms). The experimental high resolution study of the hydrogen-like excited state series of shallow levels has yielded as many as 19 lines of width as small as 10μeV for some centers. These results have stimulated theoretical work which has led to the unambiguous assignment of quantum states to many bound excited states. Extensive studies of ultra-pure Ge crystals grown under different well-controlled conditions have led to the discovery of a large number of novel shallow impurity complexes. Study of the multiplicities and symmetries of the associated electronic states has led to a detailed understanding of the unusual static and dynamic structures of these novel centers. The chemical composition has been deduced from correlations between the concentration of a particular center and the materials involved in crystal gowth. Isotopic substitution of hydrogen with deuterium has led to the unambiguous proof of the presence of hydrogen in several of the novel centers. In addition to the high resolution spectra of shallow electronic levels, vibrational spectra of bond-centered interstitial oxygen in ultra-pure Ge are noteworthy for their extraordinarily sharp lines.