NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. In this thesis an attempt is made to clarify the connection between two physically different SU(6)W algebras. The one SU(6)W is an approximate symmetry group, and leads to the idea that hadrons are composed of just a few "constituent" quarks. The other SU(6)W is an algebra of physically observable operators, integrals over various components of vector, axial, and tensor currents. These currents behave, algebraically, as if they were simple bilinear combinations of "current" quark fields. We propose that these two physically different algebras are related by a unitary transformation. This transformation is necessarily very different from the identity. We identify several properties of this transformation, and then go on to construct it explicitly in the free quark model, where it yields an exactly conserved SU(6)W symmetry of constituent quarks. We then show how this transformation may be constructed in models with interacting quarks. In general, the algebraic structure of the transformation depends upon the dynamical details of the interaction. We discuss the effect of interactions in more detail, distinguishing two cases. In one case the structure of the transformation in the interacting model need not have any relation to that of the free quark model. In the other case, the algebraic structure of the two transformations are the same. We cannot distinguish these two cases at present. However, as found in the last section, the algebraic structure of the transformed currents in nature seems to be roughly that given by the free quark model transformation. The mechanism by which this occurs is obscure at present, and we can make no clearcut distinction between the two cases. As we have indicated, the last section is devoted to the application of the algebraic structure of the free quark model transformation to the matrix elements of physical currents. We are thus led to many successful approximate relations among matrix elements, not the least of which is the recovery of the famous ratio [...].