In his third book on information retrieval, Van Rijsbergen takes readers through a number of models for it, including a vector space model, a probabilistic model, and a logical model. He shows how these and others can be described and represented in Hilbert space, formulates the reasoning within each algebraically, and explains that they depend essentially on the geometry of the information space. The geometry then, can be taken as a language for expressing the different models of information retrieval.