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Let us 'home in' now on rich clusters - not forgetting, however, that these are exceptional regions of space that evolved, probably, from 3sigma fluctuations. If they formed in a hierarchical way, their internal substructure would be destroyed during collapse and virialisation of the system.

The central cores of rich clusters, being dynamically relaxed, are less likely to retain a memory of the formation process. However, it is these regions about which most is known observationally. The dominant gravitating mass is the dark matter component. This cannot be directly observed, but the galaxies and hot gas can be used to determine the density profile of the dark matter, even though they may not themselves have the same density profile. The motions of the galaxies in principle should allow us to trace out the gravitational potential well. But in practice this is difficult because we do not know whether galactic orbits are isotropic, or else predominantly radial. These orbits may also be affected by dynamical friction on the dark matter.

The gas distribution relative to the dark matter is primarily a function of the parameter beta, equal to the ratio of the gas temperature and the virial temperature. Our best evidence on the hot gas comes from X-ray data. However, problems arise because we don't have high spectral resolution combined with high angular resolution. Moreover, the gas may be inhomogeneous, and partially supported by bulk motions rather than by thermal pressure.

A new method of tracing the overall mass distribution in clusters is now becoming feasible, at least for some systems at high redshifts. This is the detection of gravitational lensing of very faint high redshift galaxies by the mass distribution in a foreground cluster. The discovery of the so-called 'arcs', and the realization in 1987 that these are gravitationally-magnified and distorted images of distant galaxies, has been followed by further evidence that many of the background galaxies along lines of sight to rich clusters are distorted. Data of this kind in principle allow reconstruction of the projected column density of gravitating mass in the cluster. Although this technique is just beginning to be applied, it has already led to the surprising conclusion that clusters are rather more centrally condensed than was believed to be the case.

The gas is an important (and, indeed, generally the dominant) baryonic constituent of clusters. The gas-to-star ratio is of order unity in poor clusters, but up to 5 in rich clusters. It could be even substantially higher if there were a lot of gas at large radii, or in cool cloudlets. (Gas in either of these forms is hard to detect.) Although the dominant mass is the dark matter, it seems that in rich clusters the baryons contribute at least 10 percent of the total. This is in itself an interesting cosmological result: standard cosmic nucleosynthesis implies that Omegab is less than 0.1; so, even if the dark matter were entirely non-baryonic, then if Omega were equal to unity there would need to be segregation of baryons on scales as large as clusters. Whereas dissipative effects can readily account for a concentration of baryons in individual galaxies, it is less clear how they might operate on cluster scales.

X-ray data show clear evidence that the intracluster gas contains heavy elements, especially Fe. However, it is unclear whether the inferred abundance applies to the entire cluster, or only to the central regions which dominate the X-ray emission. The total nucleosynthesis requirements would obviously be less stringent in the latter case.

A further uncertainty concerns the homogeneity of intracluster gas. Different bits of gas may have been shock heated on to different adiabats - indeed this is very likely if the cluster results from successive mergers in a hierarchical cosmogony. The density profile of the gas will then be modified by effects of buoyancy and sedimentation. Inhomogeneities are needed in order to trigger thermal instability, which is strongly indicated to be important from the evidence of cooling flows (which will undoubtedly figure prominently in this conference). The fate of the cooled gas is still a mystery. Can clouds or filaments of very cool gas, with T < 104K, survive in the cluster environment? Do magnetic fields or plasma processes inhibit thermal conductivity enough to allow the observed temperature gradients, and the inferred inhomogeneities to develop and persist? Does the cool gas quickly turn into stars? If so, these stars must be of low mass, and could even be a significant part of the dark matter.

Another probe of hot gas in clusters, which has been recognized in principle for many years but is now becoming observationally useful, is the Sunyaev-Zeldovich effect. This is a measure of the product of the Thomson depth through the cluster and the electron temperature (or, equivalently, of the gas pressure if the size of the cluster is known). This effect reduces the microwave background temperature on the Rayleigh-Jeans part of the spectrum. By combining measurements of the profile of this temperature dip with X-ray maps of the cluster, the Bubble constant can in principle be measured.

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