Developments in the modelling of stellar atmospheres and results from the confrontation between calculated and observed fluxes and spectra are discussed. It is argued that, although impressive advances in the study of O-type, WR and cool star spectra have recently occurred, significant improvements should be possible with already existing methods in the analysis of, e.g., solar-type stars.

We review techniques for measuring stellar oscillations in solar-type stars. Despite great efforts, no unambiguous detections have been made. A new method, based on monitoring the equivalent widths of strong lines, shows promise but is yet to be confirmed. We also discuss several subtleties, such as the need to correct for CCD non-linearities and the importance of data weighting.

Traditional observations of the properties of stars generally provide tests of only the gross aspects of stellar structure and evolution. The limitation lies in the amount and precision of the available data of relevance to the structure of the stellar interior, i.e., the determination of stellar effective temperatures, surface composition, luminosities and, in a few cases, masses. Additional constraints on the observed stars, such as the common age and composition normally assumed for stars in clusters or multiple systems, clearly increase the information. However, detailed information on the physics and processes of stellar interiors requires more extensive data, with a dependence on stellar structure sufficiently simple to allow unambiguous interpretation. Such data are offered by observations of stellar pulsation frequencies: they can be observed with great accuracy and their dependence of stellar structure is generally well understood. In particular, the richness and precision of the observed frequencies of solar oscillation are now offering a detailed view on the interior properties of a star.

We describe the search for δ Scuti stars in the MACHO database of bulge fields. Concentrating on a sample of high amplitude δ Scutis, we examine the light curves and pulsation modes. We also discuss their spatial distribution and evolutionary status using mean colors and absolute magnitudes.

Some recent theoretical results concerning Cepheids and long-period variables are presented and compared with observations. Nonlinear pulsation calculations for select bump Cepheids are shown capable of yielding very accurate fundamental properties of these stars. The implications of the derived parameters are discussed. For the long-period variables, recent observational and theoretical results pertaining to the long-standing problem of the mode of pulsation are presented. The conflicting results point to some fundamental problem with current interpretations.

On the basis of a historical overview we outline the relevant results which allowed to approach on firm basis the physical mechanisms which govern the radial pulsation of RR Lyrae variables, revealing the astrophysical parameters which account for their limiting amplitude pulsational behavior.

Massive stars are the crossroads of many important astrophysical problems and thus a proper understanding of their evolution is very needed. They are the main sources of UV radiation, by heating the interstellar dust they produce the far-IR luminosities of galaxies. They are the precursors of Supernovae and also the main sources of nucleosynthesis. They are visible in distant galaxies and the recent observations of starbursts have shown their major role in the spectral and chemical evolution of galaxies. They begin to be observed in the galactic center and in regions of star formation around galactic nuclei.

We summarize the evolution of intermediate-mass stars, calling attention to the uncertainties related to mixing in convectively unstable regions, and to recent developments in the theory of AGB stars with envelope burning. Finally, we briefly report on the distribution of C-stars of the Large Magellanic Cloud in the Mbol-log(age) plane.

Accurate modeling of the mechanical and thermal properties of very-lowmass stars (VLMS), Brown Dwarfs (BD) and Extra-solar Giant Planets (EGP) is of prior importance for a wide range of physical and astrophysical problems, from the fundamental physics point of view to the astrophysical and cosmological implications. They provide natural laboratories to test the different theories, equations of state, nuclear reaction rates, model atmospheres aimed at describing the physics of dense and cool objects. They represent the largest stellar population in the Galaxy, and thus provide a substantial contribution to the Galactic (disk) mass budget. Finally they represent one of the most intriguing questions in our understanding of the formation of star-like objects: are planet and star formation processes really different? Is there, and if so what is, a minimum mass for the formation of star-like objects? This field has blossomed recently with the discovery of several brown dwarfs (Nakajima et al, 1995; Rebolo et al., 1995) and numerous exoplanets since 51 Pegasi (Mayor and Queloz 1995; Mayor, this conference), which provide important information to challenge the theory.

Massive stars are rapid rotators. Equatorial rotation velocities span the range vrot = 100–400 km s−1, with B stars rotating closest to their break-up speed vcrit (Howarth et al. 1997). During the last decade, many observations have revealed unusual surface abundances that may require additional internal mixing (beyond that of simple convection and overshooting) for their explanation, most important helium and nitrogen enrichment in main sequence O and B stars (Gies & Lambert 1992), in the SN 1987A progenitor (Fransson et al. 1989), and boron depletions in main sequence B stars (Venn et al. 1996). In particular the latter observations clearly point towards internal mixing and rule out a close binary origin of the abundance peculiarities (Fliegner et al. 1996). Altogether, the occurrence of some form of additional mixing responsible for altering the surface abundances in a large fraction, if not all massive stars appears to be beyond reasonable doubt, and mixing processes due to rotation are the most natural explanation.

Pop II field and globular cluster giant stars (and, to a less extent, Pop I giants) exhibit chemical anomalies which are not predicted by standard stellar evolution theory. Two hypotheses have been proposed to explain these abundance variations, namely the primordial and the evolutionary explanations. A primordial origin for intracluster abundance anomalies (see e.g. Cottrel & Da Costa 1981) would be related to inhomogeneities in the cluster material due to pollution by a prior generation of massive stars. In the evolutionary hypothesis, abundance variations would be due to nuclear and mixing processes internal to the giant stars themselves. Many good reviews exist on the subject (see e.g. Briley et al. 1994a, Kraft 1994), in which observational evidence supporting both hypotheses are presented. In this conference, Da Costa recalls the most recent observational data, and some excellent poster contributions bring essential clues to the subject.

Comparisons between models of the solar interior and sound speed profiles derived from inversions of helioseismic data have demonstrated that it is essential to include the effects of gravitational settling when calculating the structure and evolution of the Sun. Including settling should also be necessary for models of metal poor main-sequence stars and results in a substantial reduction in the ages derived for globular clusters.

In many cases it is clear that competing hydrodynamic processes, such as mass loss or rotationally driven mixing, will limit the effectiveness of gravitational separation of chemical elements. However, the quantitative details and even the relative importance of the different processes in various types of stars remains poorly understood.

For 25 years our ignorance of the physical basis of this mass loss process has been the barrier to progress in understanding horizontal branch morphology. I review some recent observational and theoretical results which may be giving us clues about the nature of the mass loss process.

The majority of all stars (Mi < 8M⊙) end their lives as white dwarfs (WD). On the tip of the Asymptotic Giant Branch (AGB) the star ejects its outer layers which become a Planetary Nebula and the stellar core evolves rapidly towards very high effective temperatures (Teff > 100 kK). When the nuclear burning in the H or He shell ceases the star enters the WD cooling sequence. The evolution starting from the AGB is separated in a H–rich and a H–deficient sequence where the latter contributes with a number fraction of ≈ 20%. In this paper we describe our recent effort in the analysis of one group of these stars, the PG 1159 stars.

For stars with masses between about 1 and 8 M⊙ the ascent of the Asymptotic Giant Branch (AGB) is the last nuclear powered evolutionary stage. Following this the stars eject a planetary nebula and fade as white dwarfs. Although only short in duration, the AGB is very important due to the nucleosynthesis which occurs. Here we briefly review the species produced and the mechanism for their production. We then discuss the current uncertainties in quantitative predictions of this nucleosynthesis, which centre on our determination of convective boundaries.

The understanding of the physics of cool white dwarfs (WD) bears important consequences for Galactic evolution and cosmological implications. The observed cutoff in the disk WD luminosity function (WDLF) yields the determination of the age of the Galactic disk, as suggested initially by Winget et aI. (1987). The recent microlensing observations toward the LMC (Alcock et al., 1996) suggest that WDs might provide a substantial fraction of the halo dark matter (Chabrier, Segretain & Méra, 1996; Adams & Laughlin, 1996). The correct analysis of these applications implies a correct WD cooling theory and reliable photometric predictions, which in turn require accurate interior and atmosphere models. Important improvement in this latter domain has been accomplished recently by Bergeron, Saumon & Wesemael (1995) and Bergeron, Wesemael & Beauchamp (1995), which yields the determination of photometric color indices and bolometric corrections down to 4000 K (see Leggett, these proceedings). In this paper, we review the most recent improvement in WD interior and cooling theory.

Computer technology now allows two dimensional (2D) simulations, with complex microphysics, of stellar hydrodynamics and evolutionary sequences, and holds the promise for 3D. Careful validation of astrophysical methods, by laboratory experiment, by critical comparison of numerical and analytical methods, and by observation are necessary for the development of simulation methods with reliable predictive capability. Recent and surprising results from isotopic patterns in pre-solar grains, 2D hydrodynamic simulations of stellar evolution, and laser tests and computer simulations of Richtmeyer-Meshkov and Rayleigh-Taylor instabilities will be discussed, and related to stellar evolution and supernovae.

As we move into the next century of stellar astronomy, it is helpful to consider the modes by which stellar astronomy has advanced in the modern era. At this conference, our attention has been focussed on precision measurement of stellar fundamental properties such as mass, luminosity, and radius. This mode of inquiry is one of several that have borne fruit. In this review, I will discuss some of the topics that have arisen here with respect to how our understanding of stellar interiors progresses through interaction between theory and observation.

One of the major achievements of astrophysics has been the demonstration that most of the chemical elements have been synthesized in stars: nucleosynthesis calculations of homogeneous and inhomogeneous big bang cosmologies show that, in comparison with the most metal-poor stars currently known, essentially no elements heavier than B existed at the era of decoupling (see e.g. Wagoner, Fowler, & Hoyle 1967; Kajino, Mathews, & Fuller 1990). Following the pioneering work on stellar nucleosynthesis by Hoyle (1946), the basic precepts and the role of stars was set down in the classic papers of Burbidge et al. (1957) and Cameron (1957), and the ensuing decades have produced a vast body of theoretical and observational effort to more fully understand the details of the process.

I discuss several current problems in understanding the chemical evolution of galaxies which have particular relevance for fundamental stellar astronomy.