Measure and metric are two fundamental concepts in measuring the size of a mathematical object. Yet there has been no systematic investigation of this relation. The book closes this gap. Contents: Measure and Outer Measure; Construction of Outer Measures; Borel Measures; Hausdorff Measures; Covering Theorems; Differentiation of Measures; Averaging Operators and Differentiation of Integrals; Lebesgue Differentiation Theorem for Integrals; Hardy-Littlewood Maximal Functions; Density of Sets; Approximate Limit and Approximate Continuity; Lipschitz Mappings; Readership: Mathematicians and graduate students in mathematics.