Molecules may be seen as playing two essential roles in the Universe: as the cosmic material which forms stars; and as a first step in building complexity which culminates in life. For the second aspect of astrobiology, it is obvious that, because of the enormous distances, galaxies are not the best hunting ground to try to understand the numerous and complex steps which could lead from the simple interstellar molecules to the genetic code. On the other hand, the panoramic views provided by molecular signals from galaxies are one of the best sources of information to grasp the essential features of star formation at galactic scales. CO is the best tracer of normal, cold molecular gas. In various types of local galaxies, its millimetre lines reveal the standard giant molecular clouds, home of `normal' massive star formation such as in most of the Milky Way. CO lines also deeply probe the most extreme, massive, dusty starbursts, especially at high redshift, without being blocked and much distorted by extinction. CO and better HCN line intensities yield good estimates of the global star formation rates. The high resolution velocity profiles of CO lines, routinely offered by heterodyne techniques, provide molecular and dynamical masses of starburst galaxies, key parameters for learning about their past and future star formation history. The great news is that such a comprehensive information about star formation is available not only for our local neighbours, but more and more up to the most distant galaxies that we see in their youth and infancy. This will be soon extended by ALMA at z 10, practically up to the frontier of the `dark ages' when the first stars and galaxies formed and the Universe was only a few percents of its present age. We are indeed living the dream of the first explorers of stellar populations in the Milky Way, by directly catching the action of successive starbursts which formed most of the stars in Milky Way sisters at various epochs of their past life up to z 2. Even farther out in space and time, through molecular lines, we watch and get insight in the most powerful starbursts in the Universe, progenitors of the most massive (elliptical) galaxies today. Disentangling their history is a basic clue for understanding the joint evolution of the most fascinating objects in the Universe: their massive dark matter halos, their stellar spheroids, their central super-massive black-holes, and the massive clusters of galaxies surrounding today the most massive ones. However, the power of molecular lines to trace star formation in galaxies is far from being limited to such climaxes, but it is almost universal even for much milder episodes in various kinds of galaxies. Even much less spectacular, some of these episodes may be of great importance for their hosts, either dwarf such as the Magellanic Clouds, or giant such as elliptical galaxies harbouring cooling flows. While CO traces the cold bulk of molecular gas, observations of rotational lines of H2 itself are spectacularly progressing with the development of space mid-infrared spectroscopy. They trace patches of warm gas in particularly active regions of starbursts, mergers, vicinities of AGN, and various types of shocks even at extra-galactic scales. CO and H2 lines should thus be major tracers of violent events in galaxy lifes, such as mergers, accretion shocks, outflows and other effects of feedback action from supernovae and AGN.
Star formation is not by far the only fascinating question of contemporary astronomy that the young extragalactic molecular astrophysics may address. Large aromatic molecules (PAHs) are recognized as an ubiquitous major component and a reservoir of carbon of the interstellar medium of most types of galaxies. They are now currently studied up to redshift at least ~ 2 in the most massive galaxies; but we have still to learn about their behaviour in the first billion years of galaxy lives. Similarly, little is known about molecular mantles in strong starbursts and at high redshift. More generally, all processes of dust surface chemistry, including H2 formation, remain challenging. The extragalactic chemistry of the deuterium is still in its infancy, together with the information it can bring about the dust-gas cycle in various galactic environments. If the current results about extragalactic interstellar chemistry appear a bit disapointing as too similar to that of the Milky Way or less rich, it could be due to our lack of sensitivity, and a reassessment with ALMA is obviously necessary. In any case, the progress expected in isotopic ratio determination will be important for a better appreciation of nucleosynthesis and the chemical evolution of various types of galaxies. Tracing molecules in AGN, in the vicinity of the nucleus, up to the molecular torus, is one of the fields which will most benefit from the gains in sensitivity and angular resolution from space or with millimetre and radio interferometry and adaptive optics. This will provide unique opportunities to probe X-ray dominated chemistry and the special properties of the molecular gas in the `molecular torus'. VLBI detections of H2O mega-masers already probe the even inner region of the accretion disk, offering a unique way of accurate determination of the mass of the super-massive black hole. Their expected extension at high redshift is very promising for a direct accurate calibration of the cosmic distance scale, and in particular the precise measurement of H0. More generally extragalactic OH and H2O mega-masers provide unique examples of radiation amplification with the most extreme cosmic scales and energies. Fully appreciating the properties of mega-masers remains challenging, as well as extending their systematic detection in the most powerful starbursts at high redshift. Molecules, such as H2 and OH, also participate in high precision spectroscopy of absorption lines at high redshift, allowing one to probe possible variations of fundamental constants such as me / mp and . The multiplication of high-z background sources, especially gamma-ray bursts, will provide new opportunities, as well as probing molecules at the interface between (proto-) galaxies and the intergalactic medium.
It is clear that the vast and rich field of molecules in galaxies will see many exciting developments in the next years and importantly contribute to the progress of the exploration of the world of galaxies and their evolution.
I owe a great debt of gratitude to Al Glassgold and Pierre Cox for their past and present close collaboration, their careful reading of the whole manuscript and numerous helpful comments and suggestions. I specially thank James Lequeux and Françoise Combes, as well as two anonymous referees, for numerous helpful comments and suggestions. I also want to thank François Boulanger, Asunciòn Fuente, George Helou, Michèle Leduc, Gary Mamon, David Merritt, Padelis Papadopoulos, Patrick Petitjean, Hélène Roussel and Phil Solomon for various help and comments.