Stellar atmospheres represent unique windows for understandingstellar, galactic and cosmic evolution by being responsible forthe emission of stellar spectra. Much progress has been made overthe years in modelling stellar atmospheres but still the modellingefforts are hampered by various, often questionable, assumptionsand approximations. This review describes promising avenues forimproving 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 calculationswith a detailed non-LTE treatment of the radiative transfer.It is argued that this is fully within the realm of possibilityon this time-scale and indeed will be necessary to complementthe expected advances on the observational side.

The most remarkable future possibilities of stellar spectroscopy and abundanceanalysis are discussed, and their consequences for the further understanding of stellar nucleosynthesis are commented on. It is argued that it will soonbe possible to put the exploration of the origin of the chemical elements andthe 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 ofdust 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 directobservational test for astronuclear physics. The reliability ofsuch determinations depends on the quality of the observationaldata, but also critically on a correct understanding of allatmospheric processes as well as on fundamental atomic andmolecular data. We illustrate this different aspects with severalrecent 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 leastthree 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 giveninitial velocity, the initial masses are larger, and/or the metallicities are lower; 2) the observed numberof red supergiants at the metallicity of the Small Magellanic Cloud (SMC) can be accounted for; 3) the observed variation of the number ratioof Wolf-Rayet to O-type stars as a function of the metallicity can be reproduced. For all these comparisonsnon-rotating models give unsatisfactory fits. Rotating models results also give interestinginsights on questions such as the origin of Be stars, the mechanisms responsible forthe huge mass loss rates undergone by the Luminous Blue Variables, the rotation ratesof pulsars, the progenitors of collapsarsand the sources of primary nitrogen at low metallicity.

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

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 createdby the Tayler-Spruit dynamofor 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 withastronuclear studies. The first example is the dredge-up process by whichnuclei synthesized in the stellar interior are brought to thesurface; the second is the production of primary sodium. Those examplesillustrate the need for a good understanding of the detailsof model calculations from both a physical and a numerical stand point.They highlight as well some of the current limitations of AGB modelpredictions.

The detailed modelling of thermonuclear runaways in novae is a greatchallenge. This paper focuses on issues where the coupling betweenthe hydrodynamic and the nuclear aspects is critical. The mixing of heavy elements at the bottom of the accreted envelope is found to bethe 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 alsodiscussed.

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 benefitastrophysics, particularly in the areas ofsupernova-core deleptonization, neutrino interactions with nuclei instellar environments, the nuclear equation of state at high temperaturesand densities, and nucleosynthesis. I will discuss the current statusof our understanding of one of these overlaps, namely electroncapture on nuclei. I will thenturn to a description of coupled-cluster theory, which is a technique of solving the nuclear many-body problem thatmay be useful for calculating selected nuclear propertiesrelevant to astrophysics.

The interpretation of many astrophysical phenomena relies on an in depthunderstanding of different areas of physics. Nuclear physics has aparticularly influential role in determining the energy and matterevolution at stellar sites. As more extensive observational data isgathered from earth and space observatories, an ever-greater demand isplaced on our knowledge of the basic physical processes that underpinastrophysical phenomena. Some of the associated challenges for nuclearphysics 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 soas 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 istaken as example and illustration for research on extremely slowand complicated reactions of astrophysical interest. Twosensitive experiments in the energy range Ec.m. = 890-2800 keV have been performed and the extrapolation to300 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 astrophysicalreaction rate has been determined with ±25% precision inthe temperature range 0.001 ≤T9≤10. From 30years of research on this reaction, some problems related toexperimental nuclear astrophysics become evident and suggestionsfor improving future works are made.

In order to understand the r-process nucleosynthesis, we evaluate theprecision required for mass and β-decayhalf-life measurements planned at future radioactive-ion-beamfacilities. To satisfy a simple requirement that we put on nuclearmodel predictions, it is concluded that the detectors for the massmeasurements must have a precision of 1σ < ~ 250 keV,and that the detectors for the half-life measurementsdemand 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 shellclosure. 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 detectordevelopments.

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 astronuclearphysics, gathered from the various contributions collected in theseproceedings, is proposed.