Abstract:
Recent developments in the determination of H0 are reviewed in the context of the 3 following questions: 1) What is required to measure an accurate value of H0? Given the wide range of H0 values quoted in the current literature, is there any evidence that the situation has changed very much at all in the last couple of decades? And 3), is a measurement of H0 accurate to 10% feasible with current observational tools? Recent results on the extragalactic distance scale are extremely encouraging. A large number of independent methods (including the latest type Ia supernova calibration by Sandage et al. 1996) appear to be converging on a value of H0 in the range of 60 to 80 km/sec/Mpc. The factor-of-two discrepancy in H0 appears to be behind us. However, all of these results underscore the importance of reducing remaining uncertainties in the Cepheid distance scale (e.g., reddening and metallicity). A summary of recent results from the HST H0 Key Project is given. At the present time, a value of H0=73 +/- 6 (statistical) +/- 8 (systematic) km/sec/Mpc is obtained. This value is based on the Cepheid calibration of several different methods including the Tully-Fisher relation, type Ia supernovae, a calibration of distant clusters tied to the Fornax cluster, and direct Cepheid distances out to about 20 Mpc. The uncertainty in this estimate will decrease as further Cepheid calibrators become available over the course of the Key Project; the goal is to measure H0 to an accuracy of 10%.

Abstract:
The Hubble constant, which measures the expansion rate, together with the total energy density of the Universe, sets the size of the observable Universe, its age, and its radius of curvature. Excellent progress has been made recently toward the measurement of the Hubble constant: a number of different methods for measuring distances have been developed and refined, and a primary project of the Hubble Space Telescope has been the accurate calibration of this difficult-to-measure parameter. The recent progress in these measurements is summarized, and areas where further work is needed are discussed. Currently, for a wide range of possible cosmological models, the Universe appears to have a kinematic age less than about 14 +/- 2 billion years. Combined with current estimates of stellar ages, the results favor a low-matter-density universe. They are consistent with either an open universe, or a flat universe with a non-zero value of the cosmological constant.

Abstract:
In this review, the status of measurements of the matter density (Omega), the vaccuum energy density or cosmological constant (Lambda), the Hubble constant (H0), and ages of the oldest measured objects (t0) are summarized. Measurements of the statistics of gravitational lenses and strong gravitational lensing are discussed in the context of limits on Lambda. Three separate routes to the Hubble constant are considered: the measurement of time delays in multiply-imaged quasars, the Sunyaev-Zel'dovich effect in clusters, and Cepheid-based extragalactic distances. Globular-cluster ages plus a new age measurement based on radioactive dating of thorium in a metal-poor star are briefly summarized. Many recent, independent dynamical measurements are yielding a low value for the matter density (omega ~ 0.2 - 0.3). A wide range of Hubble constant measurements appear to be converging in the range of 60-80 km/sec/Mpc. Particular attention is paid to sources of systematic error and the assumptions that underlie many of the measurement methods.

Abstract:
Rapid progress has been made recently toward the measurement of cosmological parameters. Still, there are areas remaining where future progress will be relatively slow and difficult, and where further attention is needed. In this review, the status of measurements of the matter density, the vacuum energy density or cosmological constant, the Hubble constant, and ages of the oldest measured objects are summarized. Many recent, independent dynamical measurements are yielding a low value for the matter density of about 1/3 the critical density. New evidence from type Ia supernovae suggests that the vacuum energy density may be non-zero. Many recent Hubble constant measurements appear to be converging in the range of 65-75 km/sec/Mpc. Eliminating systematic errors lies at the heart of accurate measurements for all of these parameters; as a result, a wide range of cosmological parameter space is currently still open. Fortunately, the prospects for accurately measuring cosmological parameters continue to increase.

Abstract:
New, large, ground and space telescopes are contributing to an exciting and rapid period of growth in observational cosmology. The subject is now far from its earlier days of being data-starved and unconstrained, and new data are fueling a healthy interplay between observations and experiment and theory. I briefly review here the status of measurements of a number of quantities of interest in cosmology: the Hubble constant, the total mass-energy density, the matter density, the cosmological constant or dark energy component, and the total optical background light.

Abstract:
We discuss the impact of possible differences in the slope of the Cepheid Period-Luminosity relation on the determination of extragalactic distances in the context of recent studies that suggest changes in this slope. We show that the Wesenheit function W = V - R x ((V-I), widely used for the determination of Cepheid distances, is expected to be highly insensitive to changes in the slope of the underlying (monochromatic) Period-Luminosity (PL) relations. This occurs because the reddening trajectories in the color-magnitude plane are closely parallel to lines of constant period. As a result W-based Period-Luminosity relations have extremely low residual dispersion, which is because differential (and total line-of-sight) reddening is eliminated in the definition of W and the residual scatter due to a star's intrinsic color/position within the Cepheid is also largely insensitive to W. Basic equations are presented and graphically illustrated, showing the insensitivity of W to changes in the monochromatic PL relations.

Abstract:
Considerable progress has been made in determining the Hubble constant over the past two decades. We discuss the cosmological context and importance of an accurate measurement of the Hubble constant, and focus on six high-precision distance-determination methods: Cepheids, tip of the red giant branch, maser galaxies, surface brightness fluctuations, the Tully-Fisher relation and Type Ia supernovae. We discuss in detail known systematic errors in the measurement of galaxy distances and how to minimize them. Our best current estimate of the Hubble constant is 73 +/-2 (random) +/-4 (systematic) km/s/Mpc. The importance of improved accuracy in the Hubble constant will increase over the next decade with new missions and experiments designed to increase the precision in other cosmological parameters. We outline the steps that will be required to deliver a value of the Hubble constant to 2% systematic uncertainty and discuss the constraints on other cosmological parameters that will then be possible with such accuracy.

Abstract:
Revolutionary advances in both theory and technology have launched cosmology into its most exciting period of discovery yet. Unanticipated components of the universe have been identified, promising ideas for understanding the basic features of the universe are being tested, and deep connections between physics on the smallest scales and on the largest scales are being revealed.

Abstract:
We present a physically motivated explanation for the observed, monotonic increase in slope, and the simultaneous (and also monotonic) decrease in the width/scatter of the Leavitt Law (the Cepheid Period-Luminosity (PL) relation) as one systematically moves from the blue and visual into the near and mid-infared. We calibrate the wavelength-dependent, surface-brightness sensitivities to temperature using the observed slopes of PL relations from the optical through the mid-infrared, and test the calibration by comparing the theoretical predictions with direct observations of the wavelength dependence of the scatter in the Large Magellanic Cloud Cepheid PL relation. In doing so we find the slope of the Period-Radius (PR) relation is c = 0.724 +/- 0.006. Investigating the effect of differential reddening suggests that this value may be overestimated by as much as 10%; however the same slope of the PR relation fits the (very much unreddened) Cepheids in IC1613, albeit with lower precision. The discussion given is general, and also applies to RR Lyrae stars, which also show similarly increasing PL slopes and decreasing scatter with increasing wavelength.

Abstract:
Hipparcos parallaxes have recently become available for a sample of Galactic Cepheids, and we have used these new distances to calibrate the Cepheid period-luminosity (PL) relation at six wavelengths (BVIJHK). Comparing these calibrations with previously published multiwavelength PL relations we find agreement to within 0.07 +/- 0.14 mag, or 4 +/- 7% in distance. Unfortunately, the current parallax errors for the fundamental pulsators (ranging in signal-to-noise = pi /sigma_pi from 0.3 to 5.3, at best) preclude an unambiguous interpretation of the observed differences, which may arise from a combination of true distance modulus, reddening and/or metallicity effects. We explore these effects and discuss their implications for the distance to the Large Magellanic Cloud (LMC) and the Cepheid-based extragalactic distance scale. These results suggest a range of LMC moduli between 18.44 +/-0.35 and 18.57 +/-0.11 mag; however, other effects on the Cepheid PL relation (e.g., extinction, metallicity, statistical errors) are still as significant as any such reassessment of its zero point.