Metric in measure spaces The book presents a systematic exposition on measure theory in metric spaces. It contains detailed definitions theorems and their proofs. Measures and outer measures are considered. Metric outer measures Borel outer measures Hausdorff measures are described. In particular Hausdorff measures on linear spaces are given. Technical details on metric spaces including covering theorems are presented. Further differentiation of measures derivatives of Radon outer measures on Euclidean spaces derivatives of Borel regular outer measures on metric spaces are described. Differentiation of integrals Lebesgue theorems are also given. Hardy Littlewood maximal functions for outer measures and for functions their estimates are presented. Then approximate limits and approximate continuity in relation with measures is described. Density of sets versus measures is considered. Lipschitz mappings their extensions differentiability questions are covered. Integration on a metric space using measures measurable mappings approximation of measurable mappings the Egorov theorems are described.