The Large Hadron Collider (LHC) has started to look for new particles and interactions at energies, probed never before. Particle physics, traditionally, has made its progress by either colliding particles at ever higher energies or by measuring particle properties with increasing precision. Physics is able to describe the world from scales as small as a fraction of an atomic nucleus up to the vast expanses of space, millions of times larger than our own galaxy. The most intriguing discoveries in high energy physics in the past two decades have not been made by using accelerators, but by observing the Universe in the `light' of many different messengers. The most startling discovery has been that the Universe's expansion is accelerating, which requires the presence of a new form of energy, called `dark energy'. We also have learned that ordinary matter, out of which we are made, only contributes a small fraction of the much more abundant, invisible and hence dark matter. Furthermore we found that neutrinos have a tiny, but non-zero mass.

Some of these discoveries can be quite easily accommodated by extending the current framework, like explaining dark matter, but others may require a new paradigm altogether, like finding the origin of dark energy. Besides the question arising from those new discoveries, there are unsolved problems within the Standard Model of particle physics itself. Theoretical elementary particle physics is in a paradoxical situation: Its standard paradigm is extremely successful in describing the fundamental constituents of our observable Universe and their interactions. However, it also predicts its own breakdown at very high energies. Since we know that it is the correct description at low energies we are forced to accept its inevitable failure at very high energies. In view of this there is a plethora of attempts to formulate a theory beyond the Standard Model (SM). Any such theory, at the same time, must reproduce the SM at low energies. Most extensions of the SM which are considered candidates for discovery at the LHC are to some degree motivated by the hierarchy problem. Some of these models are even able to accommodate the observed flavor structure. However, very few of them try to explain neutrino masses and the ckm mixings. This is the more surprising since any genuine new physics around the TeV scale which does not have a very special flavor structure should already have been discovered in flavor-violating processes such as B-decays some time ago.

One of the most exciting discoveries during recent years, was that neutrinos do oscillate, i.e. they have a mass in contradiction to the sm, where neutrinos are strictly massless. The fact that neutrinos are massive opens completely new possibilities like leptonic cp violation with interesting connections to subjects, such as the baryon asymmetry of the Universe. Here, the CP violation encountered in the decay of heavy right handed neutrinos would generate a net lepton number, which later on is converted into a non-zero baryon number via sphalerons. Neutrinos, currently, are the only known weakly interacting massive particles (WIMP) and thus they are the only known component of dark matter. We we know from Tritium endpoint measurements in combination with oscillation data, that neutrinos cannot account for all of the dark matter. It is intriguing that the mass scale of neutrinos and the energy scale of dark energy are approximately the same. Is this a pure coincidence or is there a deeper connection? We do not know and there have been some first attempts in this direction. Neutrinos, or more precisely, their super-symmetric partners may be the driving force for inflation. Thus, there is virtually no area of cosmology, where neutrinos are not involved.

Beyond that, neutrinos play a crucial role in many astro-physical phenomena. For instance, type II supernovæ which are among the most violent processes in the Universe are neutrino explosions: 99% of the gravitational binding energy of the progenitor is released in neutrinos, since they are the only particles which can escape the extremely dense and hot proto-neutron star. Thus they offer the unique possibility to look into the heart of a very dynamical and complex system. The center of a supernova is one of the very few places were extended and hot nuclear matter appears in nature. Studying neutrinos from a such an event will allow to gain invaluable insights into the equation of state of dense nuclear matter. Also, the presence of new, light and weakly coupled degrees of freedom can be constrained by observing the energy loss or cooling of the proto-neutron star. New interactions of neutrinos with matter could dramatically alter the dynamics of the visible explosion and sterile sterile neutrinos with masses in the keV range could be responsible for the observed pulsar kicks.

The observed structure of neutrino mixing, namely the existence of two large mixing angles, is very different from the quark sector. Neutrinos provide a unique window into flavor physics and allow to access a problem set which is completely orthogonal to lhc physics. High precision observation of neutrino oscillations will allow us to pin-down the neutrino mixing parameters to an unprecedented level of accuracy. Quite generically one expects connections between the observed pattern of neutrino masses and mixing and grand unified theories (GUT). The smallness of neutrino masses finds a natural explanation within the context of the seesaw mechanism which seems to point to the approximately same energy scale as unification arguments. There has been a great level of interest in the literature to explore the connection between leptogenesis and low energy observables. In some of these scenarios there is a close correspondence between the low energy cp violation observable in neutrino oscillation and the baryon asymmetry of the Universe. However, the existence of CP violation in the lepton sector can only be probed by very precise oscillation data. In order to fully exploit the potential of neutrinos to yield insights into subjects as different as inflation, the baryon asymmetry of the Universe, and dense nuclear matter, it will be of paramount importance to know as much as possible about this unique messenger.