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In these lectures I shall discuss the status of the determination of the three cosmological parameters which enter the Einstein equation and govern geometry and evolution of space-time of the Universe: the Hubble constant H0, the mass density parameter Omega and the cosmological constant lambda.

Among the three parameters, the Hubble constant is the dimensionfull quantity which sets the basic size and age of the Universe. The perennial effort to determine H0 dates back to Hubble (1925) and has a long history of disconcordance. Recent progress has done much to resolve the long-standing discrepancy concerning the extragalactic distance scale, but there are some newly revealed uncertainties in the distance scale within the Milky Way. The emphasis in this lecture is on discussion of these uncertainties.

The mass density parameter directly determines the formation of cosmic structure. So, as our understanding of the cosmic structure formation is tightened, we should have a convergence of the Omega parameter. An important test is to examine whether the Omega parameter extracted from cosmic structure formation agrees with the value estimated in more direct ways. This gives an essential verification for the theory of structure formation.

The third important parameter in the Friedmann universe is the cosmological constant Lambda. We now have some evidence for a non-zero Lambda which, if confirmed, would have most profound implications for fundamental physics. This lecture will focus on the strength of this `evidence'.

We take the normalisation

Equation 1 (1)

for the flat curvature, where lambda = Lambda / 3H20 with Lambda the constant entering in the Einstein equation. The case with Omega = 1 and lambda = 0 is referred to as the Einstein-de Sitter (EdS) universe. We often use distance modulus

Equation 2 (2)

instead of the distance dL. For conciseness, we shall omit the units for the Hubble constant, (km s-1 Mpc-1).

After the Summer Institute there appeared several important papers on the distance scale. I try to incorporate these results in this article.

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