We study measure theoretic metric invariants on metric spaces, with a view towards obtaining new invariants, which in combination can be powerful tools to describe the geometry of spaces/objects. An objective is to be able to describe the symmetry of an object via an invariant called symmetry ratio. A large range of metric spaces support these invariants. A fundamental idea in the project is to extend the classes of spaces, where it is possible to apply classical analysis tools by establishing a framework for translations and generalizations. In the other direction, we can also utilize this setup to get an influx of new ideas in the classical setting.