This book deals with the mathematical and physical foundations of intrinsic structures in non-solid phases without being limited to matter. That is, it is not restricted to fluids, gases, plasmas, degenerated matter, neutron stars, black holes, etc. Thereby the expression “non-solid” may stand for everything that could show fluid- and gas-like behavior, which ranges from real liquids and gases, via dynamically interacting agents and socioeconomic spaces, all sorts of markets, systems of sufficiently weak interaction and internal “position flexibility,” the many realms of our own universe, our neurologic apparatus or mind, artificial “thinking” or Turing machines, information units in living and non-living systems of all scales, the interaction patterns of these units, and structures with all sorts of fields (electromagnetic and other), to the so-called space-times or subspace-times of Everett worlds. Instead of associating the word “non-solid” with classical liquids and immediately resorting to the Navier–Stokes or Navier–Stokes-like equations, we consider our “non-solid” as a general ensemble of attributes and, by subjecting the latter to generalized Hamilton principles, obtain Einstein field and quantum Einstein field equations. This quantum gravitational approach leads to highly astonishing solutions and structures for suitable, non-solid systems, which, if practically realized, could produce seemingly real wonder worlds.