  The celebrated tenfold-way of Altland-Zirnbauer symmetry classes discern any
quantum system by its pattern of non-spatial symmetries. It lays at the core of
the periodic table of topological insulators and superconductors which provided
a complete classification of weakly-interacting electrons' non-crystalline
topological phases for all symmetry classes. Over recent years, a plethora of
topological phenomena with diverse surface states has been discovered in
crystalline materials. In this paper, we obtain an exhaustive classification of
topologically distinct groundstates as well as topological phases with
anomalous surface states of crystalline topological insulators and
superconductors for key space-groups, layer-groups, and rod-groups. This is
done in a unified manner for the full tenfold-way of Altland-Zirnbauer
non-spatial symmetry classes. We establish a comprehensive paradigm that
harnesses the modern mathematical framework of equivariant spectra; it allows
us to obtain results applicable to generic topological classification problems.
In particular, this paradigm provides efficient computational tools that enable
an inherently unified treatment of the full tenfold-way.
