This book explores the surprisingly rich and complex structure of free lattices. The first part of the book presents a complete exposition of the basic theory of free lattices, projective lattices, and lattices which are bounded homomorphic images of a free lattice, as well as applications of these results to other areas. This portion of the book is suitable for use in a graduate course in lattice theory or general algebra. The second part of the book contains new results about free lattices and new proofs of known results, providing the reader with a coherent picture of the fine structure of free lattices. The book closes with an analysis of algorithms for free lattices and finite lattices that is accessible to researchers in other areas and depends only on the first chapter and a small part of the second. Several open problems appear throughout the book and, for easy reference, are assembled in a section at the end. Synthesizing seventy years of research, this is the only comprehensive treatment available of the theory of free lattices. Readership Mathematicians interested in algebra and lattice theory in particular. Mathematicians with an interest in algorithms in lattice theory and their complexities. Reviews "Researchers in lattice theory will find much of interest. The comprehensive nature of this book guarantees that those interested in further research in lattices will find this book indispensable. "An extensive body of results on free lattices exists, and the twelve chapters of this book provide a comprehensive yet engaging survey of these results ... Anyone working in lattice theory or in the study of free algebraic systems should certainly have access to a copy."  Bulletin of the AMS "This scholarly text covers the fascinating subject of free lattices, the general structure of which is very complex. Beautifully set using TeX, and reasonably priced, it provides the lattice theorist with a wealth of information on the subject and is sure to become a classic reference. The reader can be assured of the quality of the exposition simply from the names of the author ... The book ends with a collection of 14 challenging open problems and a useful bibliography."  Mathematical Reviews "Well written and has an abundance of wellchosen examples."  Zentralblatt MATH "An extensive body of results on free lattices exists, and the twelve chapters of this book provide a comprehensive yet engaging survey of these results ... Anyone working in lattice theory or in the study of free algebraic systems should certainly have access to a copy."  Bulletin of the London Mathematical Society "A beautiful book which collects all what is known on free lattices!"  Monatshefte für Mathematik Table of Contents  Whitman's solution to the word problem
 Bounded homomorphisms and related concepts
 Covers in free lattices
 Day's theorem revisited
 Sublattices of free lattices and projective lattices
 Totally atomic elements
 Finite intervals and connected components
 Singular and semisingular elements
 Tschantz's theorem and maximal chains
 Infinite intervals
 Computational aspects of lattice theory
 Term rewrite systems and varieties of lattices
 Open problems
 Bibliography
 List of symbols
 Index
