Applying the geometry of generalized almost-Hermitian structures as an apparatus, a close classification of almost-contact metric manifolds is attempted. Since this apparatus stands on the concept of a Q-algebra over a ring with involution, the first chapter presents its algebraic aspect, revealing the antilinearity of the composition operators, the condition of compatibility of such operators with metrics and the spectrum of a tensor in a Q-algebra. In the second chapter, the concept of generalized almost-Hermitian structure is introduced and shows that there is a smooth manifold structure such that the fibre of its tangent bundle is just a Q- algebra. After giving in the third chapter a brief survey of almost- contact metric structures including its several subclasses, the author makes clear that the concept mentioned in the second chapter can help to generalize the ever known almost-contact metric structures to a significantly broad extent.