A general, incomplete and partisan overview of various areas of the
theoretical investigation is presented. Most of this activity stems from the
search for physics beyond quantum field theory and general relativity, a
titanic struggle that, in my opinion, empowered the symmetry principles to a
dangerous level of speculation. In the works (that are my own) commented upon
here the attempt has been to proceed by holding to certain epistemological
pillars (usually absent from the too speculative theories) such as, e.g., four
or less dimensions, proposals for experimental tests of radical ideas, wide
cross-fertilization, etc.. As for the latter, the enterprise is undertaken
within a theoretical perspective that pushes till condensed matter and even
biology the cross-fertilization between ``branches of physics''.Comment: 42 pages, 1 figure, Habilitation (associate professorship)
dissertation at Charles University in Prague, the papers of Section 5 are not
included but easy to fin