The subject of the book is the relationship between definable forcing and descriptive set theory. The forcing serves as a tool for proving independence of inequalities between cardinal invariants of the continuum. The analysis of the forcing from the descriptive point of view makes it possible to prove absoluteness theorems of the type “certain forcings are the provably best attempts to achieve consistency results of certain syntactical form” and others. There are connections to such fields as pcf theory, effective descriptive set theory, determinacy and large cardinals, Borel equivalence relations, abstract analysis, and others.