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 Boolean, Vector Space and probabilistic methods, but also Web retrieval algorithms like PageRank, HITS, and SALSA 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 Dominichs presentation is characterized by an engineering-like approach, describing all methods and technologies with as much mathematics as needed for clarity and exactness. His readers in both computer science and mathematics will learn how one single concept can be used to understand the most important retrieval methods, to propose new ones, and also to gain new insights into retrieval modeling in general. Thus, his book is appropriate for researchers and graduate students, who will additionally benefit from the many exercises at the end of each chapter.