Abstract:
In this article I review the main methods for determining the age of the Universe. I describe how to determine the age of the oldest known systems at z=0, the system of galactic globular clusters, using different techniques. I also describe how to date the Universe using the decay of radioactive elements (Cosmochronology). Finally, I focus on how to determine the age of the Universe at different redshifts and specially the age of radio-quiet galaxies at high redshift. I finish by arguing that the most probable age for the Universe is $14 \pm 2$ Gyr.

Abstract:
I review the statistical techniques needed to extract information about physical parameters of galaxies from their observed spectra. This is important given the sheer size of the next generation of large galaxy redshift surveys. Going to the opposite extreme I review what we can learn about the nature of the primordial density field from observations of high--redshift objects.

Abstract:
I present a biased review of when the epoch of formation of galaxies (both disks and ellipticals) maybe took place. I base my arguments in simple (mostly) analytic models that have been recently developed to reproduce most of the observed photometric, chemical and dynamical properties of galaxies both at low and high redshift.

Abstract:
From recent CMB and Large Scale Structure observations the value of the equation of state of dark energy, assuming it to be constant in time, is constrained to be -1.3

Abstract:
There has been significant recent progress in observational cosmology. This, in turn, has provided an unprecedented picture of the early universe and its evolution. In this review I will present a (biased) view of how one can use these observational results to constraint fundamental physics and in particular physics beyond the standard model.

Abstract:
We extend our previous method to determine globular cluster ages using the luminosity function (Jimenez \& Padoan 1996). We show that the luminosity function depends on both age and distance modulus and that it is possible to distinguish between the two. This method provides at the same time independent determinations of distance and age of a GC by simply counting the number of stars found inside specified luminosity bins. The main uncertainties in other traditional methods for determining GCs ages are absent (e.g. mixing length, color-$T_{\rm eff}$ calibration, morphology of the color-magnitude diagram ). The distance modulus is the biggest uncertainty in determining the age of GCs. Here we show that the age can be determined with small uncertainty for any value of distance modulus using the LF and that the LF allows a determination of the distance modulus itself. This is explained by the fact that the luminosity function is affected by a change in distance-modulus in a way that is different from its time evolution. If GC stellar counts with statistical errors not larger than $3\%$ are available, the age can be determined with an uncertainty of about 0.4 Gyr (independent of distance modulus, mixing length and color calibration) and the distance modulus with an uncertainty of about 0.04 mag.

Abstract:
We have used the Hipparcos satellite colour magnitude diagram to determine the age of the Galactic disc. We first measure the metallicities of Hipparcos giants using DDO photometry (H{\o}g & Flynn 1997). With accurate metallicities and distances we compute the minimum age of the Galactic disc as $11\pm1$ Gyr using the colour of the reddest clump stars as a function of metallicity. In conjunction with the new ages derived for Globular Clusters using the same method (Jimenez et al 1996) we show that any delay between the formation of the halo and the disc was only 2-3 Gyr. Since disc galaxies may have been detected to redshifts as high as $z=3.15$ (Lu, Sargent and Barlow 1997) an age for our own Galactic disc of 11 Gyr favours open or non-zero $\Lambda$ cosmological models. We show that a Reimers mass-loss law is sufficient to explain the morphology of the red clump.

Abstract:
We present a new method to compute stellar ages in Globular Clusters (GC) that is ten times more precise than the traditional isochrone fitting procedure. The method relies on accurate stellar evolutionary tracks and on photometry for GCs complete down to the main sequence, and it is based on counting number of stars in two different regions of the CMD: the red giant branch and the main-sequence. We have applied this method to the globular cluster M68 and found an age of 16.4$\pm$0.2 Gyr for $(m-M)_V=15.3$. This new method reduces the error associated to the uncertainty in the distance modulus by a factor of two, the error due to the choice of the value for the mixing length parameter to almost zero and the error due to the colour-$T_{\rm eff}$ transformation to zero.

Abstract:
We propose to use relative galaxy ages as a means of constraining cosmological parameters. By measuring the age difference between two ensembles of old galaxies at somewhat different redshifts, one could determine the derivative of redshift with respect to cosmic time, dz/dt. At high redshifts, z=1-2, this measurement would constrain the equation-of-state of the dark energy, while at low redshifts, z< 0.2, it would determine the Hubble constant, H_0. The selected galaxies need to be passively-evolving on a time much longer than their age difference.