Abstract: Symmetries in the Physical Laws of Nature lead to observable effects. Beyond the regularities and conserved magnitudes, the last few decades in particle physics have seen the identification of symmetries, and their well-defined breaking, as the guiding principle for the elementary constituents of matter and their interactions. Flavour SU(3) symmetry of hadrons led to the Quark Model and the antisymmetric requirement under exchange of identical fermions led to the colour degree of freedom. Colour became the generating charge for flavour-independent strong interactions of quarks and gluons in the exact colour SU(3) local gauge symmetry. Parity Violation in weak interactions led us to consider the chiral fields of fermions as the objects with definite transformation properties under the weak isospin SU(2) gauge group of the Unifying Electro-Weak SU(2) x U(1) symmetry, which predicted novel weak neutral current interactions. CP-Violation led to three families of quarks opening the field of Flavour Physics. Time-reversal violation has recently been observed with entangled neutral mesons, compatible with CPT-invariance. The cancellation of gauge anomalies, which would invalidate the gauge symmetry of the quantum field theory, led to Quark-Lepton Symmetry. Neutrinos were postulated in order to save the conservation laws of energy and angular momentum in nuclear beta decay. After the ups and downs of their mass, neutrino oscillations were discovered in 1998, opening a new era about their origin of mass, mixing, discrete symmetries and the possibility of global lepton-number violation through Majorana mass terms and Leptogenesis as the source of the matter-antimatter asymmetry in the universe. The experimental discovery of quarks and leptons and the mediators of their interactions, with physical observables in spectacular agreement with this Standard Theory, is the triumph of Symmetries. The gauge symmetry is exact only when the particles are massless. One needs a subtle breaking of the symmetry, providing the origin of mass without affecting the excellent description of the interactions. This is the Brout-Englert-Higgs Mechanism, which produces the Higgs Boson as a remnant, discovered at CERN in 2012. Open present problems are addressed with by searching the New Physics Beyond-the-Standard-Model.

Abstract: The search for dark matter is one of the hottest topics in Physics today. The fact that about 80% of the matter of the Universe is of unknown nature has triggered an intense experimental activity to detect this kind of matter and a no less intense effort on the theory side to explain it. Given the fact that we do not know the properties of dark matter well, searches from different fronts are mandatory. Neutrino telescopes are part of this experimental quest and offer specific advantages. Among the targets to look for dark matter, the Sun and the Galactic Center are the most promising ones. Considering models of dark matter densities in the Sun, neutrino telescopes have put the best limits on spin-dependent cross section of proton-WIMP scattering. Moreover, they are competitive in the constraints on the thermally averaged annihilation cross-section for high WIMP masses when looking at the Galactic Centre. Other results are also reviewed.

Abstract: The primary scientific goal of neutrino telescopes is the detection and study of cosmic neutrino signals. However, the range of physics topics that these instruments can tackle is exceedingly wide and diverse. Neutrinos coming from outside the Earth, in association with other messengers, can contribute to clarify the question of the mechanisms that power the astrophysical accelerators which are known to exist from the observation of high-energy cosmic and gamma rays. Cosmic neutrinos can also be used to bring relevant information about the nature of dark matter, to study the intrinsic properties of neutrinos and to look for physics beyond the Standard Model. Likewise, atmospheric neutrinos can be used to study an ample variety of particle physics issues, such as neutrino oscillation phenomena, the determination of the neutrino mass ordering, non-standard neutrino interactions, neutrino decays and a diversity of other physics topics. In this article, we review a selected number of these topics, chosen on the basis of their scientific relevance and the involvement in their study of the Spanish physics community working in the KM3NeT and ANTARES neutrino telescopes.