Stellar atmospheres represent unique windows for understanding stellar, galactic and cosmic evolution by being responsible for the emission of stellar spectra. Much progress has been made over the years in modelling stellar atmospheres but still the modelling efforts are hampered by various, often questionable, assumptions and approximations. This review describes promising avenues for improving the realism of stellar model atmospheres for hot (spectral types O, B, A), cool (F, G, K) and very cool (M and later) stars, respectively, in the coming decade. A common theme will be time-dependent 3D hydrodynamical calculations with a detailed non-LTE treatment of the radiative transfer. It is argued that this is fully within the realm of possibility on this time-scale and indeed will be necessary to complement the expected advances on the observational side.

The most remarkable future possibilities of stellar spectroscopy and abundance analysis are discussed, and their consequences for the further understanding of stellar nucleosynthesis are commented on. It is argued that it will soon be possible to put the exploration of the origin of the chemical elements and the study of the chemical evolution of galaxies on a solid empirical ground, through systematic observations of yields from AGB stars and planetary nebulae, Wolf-Rayet stars and supernovae, and of well-determined abundance trends in different stellar populations.

Dust forming systems, in which a phase transition between the gas phase and the solid state takes place, are seriously affected by the presence of dust, which causes tight, non-linear interactions between various physical and chemical processes. As a consequence, the dynamics of, e.g., a stellar atmosphere and the formation of dust grains are inseparably connected. Chemical conditions, dust formation, and dust-induced instabilities in such non-linearly coupled systems as well as some implications regarding stellar evolution are discussed.

The determination of stellar abundances is the most direct observational test for astronuclear physics. The reliability of such determinations depends on the quality of the observational data, but also critically on a correct understanding of all atmospheric processes as well as on fundamental atomic and molecular data. We illustrate this different aspects with several recent examples which served as a general introduction to the "round table" on this subject.

The inclusion of rotation in massive star models improves the agreement between theory and observations on at least three important points: 1) rotational mixing allows to produce variations of the surface abundances already during the Main-Sequence phase as is observed. The changes of the surface abundances are more important when, for a given initial velocity, the initial masses are larger, and/or the metallicities are lower; 2) the observed number of red supergiants at the metallicity of the Small Magellanic Cloud (SMC) can be accounted for; 3) the observed variation of the number ratio of Wolf-Rayet to O-type stars as a function of the metallicity can be reproduced. For all these comparisons non-rotating models give unsatisfactory fits. Rotating models results also give interesting insights on questions such as the origin of Be stars, the mechanisms responsible for the huge mass loss rates undergone by the Luminous Blue Variables, the rotation rates of pulsars, the progenitors of collapsars and the sources of primary nitrogen at low metallicity.

We examine the effect of binary companions and magnetic fields on stellar evolution. Today our understanding of the former is good though far from complete. We single out common envelope evolution as the least satisfactory and illustrate the effects of our lack of knowledge on the population synthesis of type Ia supernovae. We currently fare much worse with magnetic fields and so concentrate on what we do know and where this breaks down. Combining both aspects we examine what role magnetic fields might play in common envelope evolution.

Rotation and mass loss appear to resolve many problems remaining in the evolution of massive stars. But, we may wonder whether magnetic fields are important or not. Some first effects of the magnetic fields created by the Tayler-Spruit dynamo for massive stars are shown. As it stands presently, the theory does not agree well with observations. Thus, either magnetic fields are of little importance in massive stars or the dynamo theory needs to be further improved.

Two examples of stellar predictions from models of asymptotic giant branch (AGB) stars are presented to illustrate the difficulties associated with astronuclear studies. The first example is the dredge-up process by which nuclei synthesized in the stellar interior are brought to the surface; the second is the production of primary sodium. Those examples illustrate the need for a good understanding of the details of model calculations from both a physical and a numerical stand point. They highlight as well some of the current limitations of AGB model predictions.

The detailed modelling of thermonuclear runaways in novae is a great challenge. This paper focuses on issues where the coupling between the hydrodynamic and the nuclear aspects is critical. The mixing of heavy elements at the bottom of the accreted envelope is found to be the most significant problem. Other issues related to the modelling of the mixing at the outer parts of the convective zone and to the details of the early light curve are also discussed.

Recent progress in modeling type Ia supernovae by means of 3-dimensional hydrodynamic simulations as well as several of the still open questions are addressed. Our models are based on the assumption that thermonuclear burning inside a Chandrasekhar-mass C+O white dwarf is similar to turbulent chemical combustion and that, thus, thermonuclear supernovae can be modeled by means of numerical methods which have been developed and tested for laboratory and technical flames. It is shown that the new models have considerable predictive power and allow to study observable properties of type Ia supernovae, such as their light curves and spectra, without adjustable non-physical parameters, and they make firm predictions for the nucleosynthesis yields from the explosions. This raises a quest for better data, covering the spectroscopical and photometric evolution in all wave bands from very early epochs all the way into the nebular phase. First such results obtained by the European Supernova Collaboration (ESC) for a sample of nearby SNe Ia and their implications for constraining the models and systematic differences between them are also discussed.

We demonstrate the important role of anisotropic neutrino radiation on the mechanism of core-collapse supernova explosions. Through a newparameter study with a fixed radiation field of neutrinos, we show thatprolate explosions caused by globally anisotropic neutrino radiationrepresent the most effective mechanism of increasing the explosionenergy when the total neutrino luminosity is given. This is suggestive ofthe fact that the expanding materials of SN 1987A have a prolategeometry.

I discuss the current state of low-energy nuclear theory and the scientific questions that will be addressed over the next ten years as we move to the description of increasingly unstable nuclei. Much of our understanding of unstable nuclei will directly benefit astrophysics, particularly in the areas of supernova-core deleptonization, neutrino interactions with nuclei in stellar environments, the nuclear equation of state at high temperatures and densities, and nucleosynthesis. I will discuss the current status of our understanding of one of these overlaps, namely electron capture on nuclei. I will then turn to a description of coupled-cluster theory, which is a technique of solving the nuclear many-body problem that may be useful for calculating selected nuclear properties relevant to astrophysics.

The interpretation of many astrophysical phenomena relies on an in depth understanding of different areas of physics. Nuclear physics has a particularly influential role in determining the energy and matter evolution at stellar sites. As more extensive observational data is gathered from earth and space observatories, an ever-greater demand is placed on our knowledge of the basic physical processes that underpin astrophysical phenomena. Some of the associated challenges for nuclear physics are outlined in this paper.

I discuss a few selected topics on nucleosynthesis and nucleo-cosmochronology in faint, if not totally illusory, hopes of helping to gain a clear perspective of the future astronuclear physics. First I illustrate a few puzzles that remain to be solved by observational astronomy, theoretical astrophysics, and some nuclear physics experiments so as to promote the understanding of nucleosynthesis from the early universe till to-day. Next I pick a few exemplifying cases of difficult problems to which the study of stellar evolution and nucleosynthesis is facing up. Finally I make an attempt of putting nucleo-cosmochronology in perspective. Admittedly, some of my comments will be "politically incorrect".

The key reaction 12C(α,γ)16O is taken as example and illustration for research on extremely slow and complicated reactions of astrophysical interest. Two sensitive experiments in the energy range Ec.m. = 890-2800 keV have been performed and the extrapolation to 300 keV of the S-factors obtained by an R-matrix analysis are SE1300 =(77 ± 17)keV b; SE2300=(81±22)keV b; Stot300 = (162 ± 40) keV b. The astrophysical reaction rate has been determined with ±25% precision in the temperature range 0.001 ≤T9≤10. From 30 years of research on this reaction, some problems related to experimental nuclear astrophysics become evident and suggestions for improving future works are made.

In order to understand the r-process nucleosynthesis, we evaluate the precision required for mass and β-decay half-life measurements planned at future radioactive-ion-beam facilities. To satisfy a simple requirement that we put on nuclear model predictions, it is concluded that the detectors for the mass measurements must have a precision of 1σ < ~ 250 keV, and that the detectors for the half-life measurements demand a precision of 1σ < ~ 0.15 ms. The above two specifications are required at the neutron richness of A/Z = 3.0 at the N=82 shell closure and A/Z = 2.9 at the N=50 shell closure. For the doubly magic nuclide 78Ni, a precision of 1σ < ~ 300 keV and 1σ < ~ 5 ms are required, respectively, for mass and half-life measurements. This analysis aims at providing a first rough guide for ongoing detector developments.

γ-ray sources at synchrotron radiation facilities will provide unprecedented opportunities to investigate photonuclear reactions of astrophysical interest. I report recent research activities in Japan and call for an international collaboration to construct a photonuclear astrophysics database.

A non-exhaustive list of open problems in the field of astronuclear physics, gathered from the various contributions collected in these proceedings, is proposed.