Introduction to Lattices and Order, 2nd edn
The primary aim of this second edition is to serve as a textbook devoted to ordered sets and lattices and to their contemporary applications. The level is suitable for advanced undergraduate and first-year graduate students. The only prerequisites are a knowledge of elementary abstract algebra and the notation of set theory.
Starting with elementary concepts of ordered sets, lattices and complete lattices, the book proceeds to a brief description of formal concept analysis, to elements of the structure theory of lattices and of their representations in the finite case. Several topics important for theoretical computer science are also studied, including Galois connection, fixed-point theorems for ordered sets, and applications of domains in information systems. The book contains numerous exercises and reflects the lively lecturing style of both authors. It can be recommended as a valuable source to anyone who needs to use ordered structures in any context.