This book is devoted to some topics of the general theory of invariant and quasi-invariant measures. Such measures are usually defined on various σ-algebras of subsets of spaces equipped with transformation groups, and there are close relationships between purely algebraic properties of these groups and the corresponding properties of invariant (quasi-invariant) measures. The main goal of the book is to investigate several aspects of those relationships (primarily from the set-theoretical point of view). Also of interest are the properties of some natural classes of sets, important from the viewpoint of the theory of invariant (quasi-invariant) measures.Contents:Some Properties of Transformation GroupsQuasiinvariant and Invariant MeasuresSome Examples and ConstructionsNonmeasurable Sets with Respect to Quasiinvariant and Invariant MeasuresSmall Sets with Respect to Quasiinvariant MeasuresAlmost Invariant SetsSome Invariant σ-Ideals and σ-AlgebrasDensity Points and Invariant Extensions of Lebesgue MeasureThe Uniqueness of Lebesgue and Borel MeasuresQuasiinvariant Borel Measures on Standard GroupsReadership: Pure mathematicians.Key Features:Presents a shift in the scientific paradigm to accommodate large scale computationAddresses the problem of climate change and global warming in a scientific mannerExplains the link between a shift in the scientific paradigm and the misunderstandings of climate change