Gratzer G. Lattice Theory. Speciaics and Applications Vol 2. 2016

Textbook in PDF format

George Grätzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Grätzer considered updating the second edition to reflect some exciting and deep developments. He soon realized that to lay the foundation, to survey the contemporary field, to pose research problems, would require more than one volume and more than one person.
So Lattice Theory: Foundation provided the foundation. Now we complete this project with Lattice Theory: Special Topics and Applications, in two volumes, written by a distinguished group of experts, to cover some of the vast areas not in Foundation.
This second volume is divided into ten chapters contributed by K. Adaricheva, N. Caspard, R. Freese, P. Jipsen, J.B. Nation, N. Reading, H. Rose, L. Santocanale, and F. Wehrung.
Varieties of Lattices
Free and Finitely Presented Lattices
Classes of Semidistributive Lattices
Lattices of Algebraic Subsets and Implicational Classes
Convex Geometries
Bases of Closure Systems
Permutohedra and Associahedra
Generalizations of the Permutohedron
Lattice Theory of the Poset of Regions
Finite Coxeter Groups and the Weak Order