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This book takes a unique approach to information retrieval by laying down the foundations for a modern algebra of information retrieval based on lattice theory. All major retrieval methods developed so far are described in detail ئ Boolean, Vector Space and probabilistic methods, but also Web retrieval algorithms like PageRank, HITS, and SALSA ئ and the author shows that they all can be treated elegantly in a unified formal way, using lattice theory as the one basic concept. Further, he also demonstrates that the lattice-based approach to information retrieval allows us to formulate new retrieval methods. Sándor Dominichѫs presentation is characterized by an engineering-like approach, describing all methods and technologies with as much mathematics as needed for clarity and exactness.