These lecture notes deal with the problem of collective coordinates in many-body systems, which are treated as gauge systems in (0+1) dimensions. The resulting classical Dirac brackets are discussed, as well as the structure of the quantal space of wavefunctions. Emphasis is made on the application of the BRST formalism. Several systems displaying an approximate breakdown of symmetries are treated. Many-body physicists may find attractive both a rigorous formulation of the problem of collective coordinates and being introduced to the BRST formalism, which has become a fundamental tool in gauge theories. Field-theorists may find illuminating the applications to simpler mechanical examples. The notes are self-contained. In particular, they do not require a previous knowledge of either the BRST formalism or of collective transformations.Contents:IntroductionThe Classical Treatment of Systems Described by Means of Collective CoordinatesThe Hilbert Spaces Associated with Collective CoordinatesThe BRST TreatmentThe Quantification Procedure of Faddeev-PopovThe Breaking and the Restoration of SymmetriesThe Application of the BRST Formalism to Abelian TransformationsThe Rotational Transformations in Three DimensionsThe Collective DynamicsReadership: Condensed matter, high energy, quantum mechanics and nuclear physicists.Key Features:An annual publication that provides a critical look at various challenges that Singapore facesContributed by independent scholars, academics and civil servants