A number of results related to the central notion of absolute measurable spaces, or universal measurability, is presented. A separable metrizable space is called absolutely measurable (or absolutely null) if its homeomorphic embedding to any separable metrizable space Y is measurable (null) with respect to every complete continuous finite Borel measure on Y. The relative notions for subsets of a given separable metrizable space are called universally measurable and universally null sets. Let us roughly indicate some of the more concrete main topics covered by the book. Results showing the existence of universally null sets, which are big with respect to cardinality, the Hausdorff dimension and topological dimension appear in chapters 1, 5 and 6. The possibility of testing universal measurability by a smaller family of measures, namely by so-called positive measures, or by the homeomorphic transforms of a particular measure in concrete spaces (e.g. in n-dimensional manifolds) is discussed thoroughly in chapters 2 and 3 and some results are applied in chapter 4. The appendices cover most of the needed preliminaries.