Introduction to lattices and order.
2nd ed.

*(English)*Zbl 1002.06001
Cambridge: Cambridge University Press. xii, 298 p. (2002).

The second edition is substantially different from the original one published in 1990 (see Zbl 0701.06001). It is an excellent textbook on ordered sets and lattices and it is intended for undergraduate and beginning graduate students in mathematics. A basic theory of order and lattices accessible to the students is given. The textbook shows the importance of the concept of order in algebra, logic, computer science and other fields. Many examples that illustrate this can be found here.

The textbook is divided into 11 chapters: Ordered sets, Lattices and complete lattices, Formal concept analysis, Modular, distributive and Boolean lattices, Representation: the finite case, Congruences, Complete lattices and Galois connections, CPOs and fixpoint theorems, Domains and informations systems, Maximality principles, Representation: the general case. Each chapter is followed by exercises (there are 273 exercises). The book ends with two appendices. Appendix A provides a very concise summary of the results from topology needed in the last chapter. Appendix B gives references and suggestions for further reading.

The textbook is divided into 11 chapters: Ordered sets, Lattices and complete lattices, Formal concept analysis, Modular, distributive and Boolean lattices, Representation: the finite case, Congruences, Complete lattices and Galois connections, CPOs and fixpoint theorems, Domains and informations systems, Maximality principles, Representation: the general case. Each chapter is followed by exercises (there are 273 exercises). The book ends with two appendices. Appendix A provides a very concise summary of the results from topology needed in the last chapter. Appendix B gives references and suggestions for further reading.

Reviewer: Vaclav Slavic (Praha)

##### MSC:

06-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordered structures |