Stellar ages have traditionally been used to constrain cosmological models by setting lower limits to the age of the universe. We quickly review the basic cosmological concepts that underpin the derivation of a finite age, and the constraints given by the measure of cosmological parameters at a redshift z ∼ 1000. The most direct way of measuring stellar ages through the abundance of radioactive elements is shown to suffer from systematics in the evaluation of the production ratios, to the extent that the constrains are less stringent that previously thought. The discrepancy between the ages of the oldest stars and the cosmologically inferred age of the universe may well be dominated by systematc effects in the predicted evolution of low-mass stars.

During these past decades, our knowledge of evolutionary and structural properties of stars of different mass and chemical composition is significantly improved. This result has been achieved as a consequence of our improved capability in understanding and describing the physical behaviour of matter in the different thermal regimes characteristic of the various stellar mass ranges and evolutionary stages. This notwithstanding, the current generation of stellar models is still affected by significant and, usually, not negligible uncertainties. These uncertainties are related to our poor knowledge of some physical proceses occurring in the real stars such as, for instance, some thermodynamical processes, nuclear reaction rates, as well as the efficiency of mixing processes. These drawbacks of stellar models have to be properly taken into account when comparing theory with observations in order to derive relevant information about the properties of both resolved and unresolved stellar populations. On the other hand, observations of both field and cluster stars can provide fundamental benchmarks for constraining the reliability and accuracy of the theoretical framework. In the following we review some important evolutionary and structural properties of very-low and low-mass stars, as well as the most important uncertainties affecting the stellar models for such stars. We show what are the main sources of uncertainty along the main evolutionary stages, and discuss the present level of agreement between theory and observations.

We present the basic concepts necessary to build atmosphere models for any type of star. We then illustrate how atmosphere models can be used to determine stellar parameters. We focus on the effects of line-blanketing for hot stars, and on non-LTE and three dimensional effects for cool stars. We illustrate the impact of these effects on the determination of the ages of stars from the HR diagram.

Among the various methods used to age-date stars, methods based on stellar model predictions are widely used, for nearly all kind of stars in large ranges of masses, chemical compositions and evolutionary stages. The precision and accuracy on the age determination depend on both the precision and number of observational constraints, and on our ability to correctly describe the stellar interior and evolution. The imperfect input physics of stellar models as well as the uncertainties on the initial chemical composition of stars are responsible for uncertainties in the age determination. We present an overview of the calculation of stellar models and discuss the impact on age of their numerous inputs.

Accurate and precise stellar ages are best determined for stars which are strongly observationally constrained, that is which are intrinsically oscillating. We review here the seismic diagnostics which are sensitive to stellar ages and provide some illustrating examples of seismically age-dated stars.

Stellar evolution theory has been extraordinarily successful at explaining the different phases under which stars form, evolve and die. While the strongest constraints have traditionally come from binary stars, the advent of asteroseismology is bringing unique measures in well-characterised stars. For stellar populations in general, however, only photometric measures are usually available, and the comparison with the predictions of stellar evolution theory have mostly been qualitative. For instance, the geometrical shapes of isochrones have been used to infer ages of coeval populations, but without any proper statistical basis. In this chapter we provide a pedagogical review on a Bayesian formalism to make quantitative inferences on the properties of single, binary and small ensembles of stars, including unresolved populations. As an example, we show how stellar evolution theory can be used in a rigorous way as a prior information to measure the ages of stars between the Zero Age Main Sequence and the Helium flash, and their uncertainties, using photometric data only.

It takes years of effort employing the best telescopes and instruments to obtain high-quality stellar photometry, astrometry, and spectroscopy. Stellar evolution models contain the experience of lifetimes of theoretical calculations and testing. Yet most astronomers fit these valuable models to these precious datasets by eye. We show that a principled Bayesian approach to fitting models to stellar data yields substantially more information over a range of stellar astrophysics. We highlight advances in determining the ages of star clusters, mass ratios of binary stars, limitations in the accuracy of stellar models, post-main-sequence mass loss, and the ages of individual white dwarfs. We also outline a number of unsolved problems that would benefit from principled Bayesian analyses.

The rotation rate, level of magnetic activity and surface lithium abundance are age-dependent quantities in stars of about a solar mass and below. The physical reasons for the evolution of these phenomena are qualitatively understood, but accurate quantitative models remain dependent on empirical calibration using the Sun and stars of known age, chiefly in clusters. In this work I review the status of these “empirical age indicators”, outlining the astrophysics of their time dependence, describing the measurements, assessing the precision (and accuracy) of age estimates when applied to individual stars, and identifying their principle limitations in terms of the mass and age ranges over which they are useful. Finally, I discuss the “lithium depletion boundary” technique which, in contrast to the empirical methods, appears to provide robust, almost model-independent ages that are both precise and accurate, but which is only applicable to coeval groups of stars.

Studying exoplanets with their parent stars is crucial to understand their population, formation and history. We review some of the key questions regarding their evolution with particular emphasis on giant gaseous exoplanets orbiting close to solar-type stars. For masses above that of Saturn, transiting exoplanets have large radii indicative of the presence of a massive hydrogen-helium envelope. Theoretical models show that this envelope progressively cools and contracts with a rate of energy loss inversely proportional to the planetary age. The combined measurement of planetary mass, radius and a constraint on the (stellar) age enables a global determination of the amount of heavy elements present in the planet interior. The comparison with stellar metallicity shows a correlation between the two, indicating that accretion played a crucial role in the formation of planets. The dynamical evolution of exoplanets also depends on the properties of the central star. We show that the lack of massive giant planets and brown dwarfs in close orbit around G-dwarfs and their presence around F-dwarfs are probably tied to the different properties of dissipation in the stellar interiors. Both the evolution and the composition of stars and planets are intimately linked.

In this contribution we illustrate how the knowledge of the ages of stars is important to constrain star formation processes. We focus on two specific cases: star formation around the supermassive black hole at the center of the Galaxy and triggered star formation on the borders of Hii regions.

Present studies on the evolution of the Milky Way are driven and shaped by how we conceive its stellar populations, in an on going process started by W. Baade seventy years ago. Despite much progress and advances in our understanding of these populations, inspection of their main properties is however hardly indicative of the path the Milky Way has followed to build up its mass. This is not only a matter of (stellar) age measurement, but more so the consequence of how we interprete the structures that we see in our Galaxy, often through the filter of our definitions of stellar populations. The panorama presented in the following pages opens the possibility that the present “filter” is not fully adequate. I start these Lectures with a summary of the main properties of the disks, bulge, and halo, and then present some of the new directions in the interpretation of the structure and evolution of the disk(s), with emphasis on chemical evolution. I discuss recent results in our understanding of the bulge, its stellar components and chemical evolution. Finally, I present the ideas currently proposed to explain the formation of the Galactic stellar halo. I conclude by examining how deeply all these new results question our present definition of stellar populations.