This is a greatly revised and expanded version of the book Cardinal fu- tionsonBooleanalgebras,Birkh auser1990.Knownmistakesinthatbookhave beencorrected,andmanyoftheproblemsstatedtherehavesolutionsinthepresent treatment. At the same time, many new problems are formulated here; some as development of the solved problems from the earlier work, but most as a result of more careful study of the notions. The book is supposed to be self-contained, and for that reason many classical results are includ ...