Water is fascinating in all its phases, forms and states of aggregation. It may look simple, just two hydrogen atoms and one oxygen atom, as we all learned in school, yet its many puzzling properties are still not completely understood. In particular, what is really missing is a microscopically based understanding of the origin of the many water anomalies. Although we know what happens, for instance, if water in a glass bottle is left in the freezer, we have imperfect understanding of the molecular origin of the anomalous density maximum that eventually determines the expansion of water and the breaking of the bottle.

The situation is even more intriguing and consequential, as it is fair to state that the possibility of life on our planet is strongly coupled to this particular anomalous behavior of water, namely the fact that ice, being less dense than water, floats in the oceans at the Earth's poles. This fact has far-reaching consequences. It plays a major role in determining the climate on our planet, it allows the diffusion of nutrients in the sea, and finally permits all human activities based on extracting resources from a liquid ocean, to name but a few. We could then easily resonate with Paracelsus who, in the 16th century, said “water was the matrix of the world and of all its creatures”. Five centuries later, we certainly know quite a bit more about water than Paracelsus, but our understanding of water's properties, both as a pure substance and as a solvent, is still far from being complete.

Our proposal to organize a school on the complexity of water in the beautiful setting of Villa Monastero in Varenna was, therefore, aimed at presenting to interested students several examples of ongoing research on water. Our intention was to offer a glimpse on the many questions that remain to be understood about this molecule. Distinguished scientist were selected to lecture on what we think is the present state of the art, along with current controversies, pertaining to our knowledge on water. The list of topics is by no means exhaustive or complete, and probably reflects more our interests and tastes, but we believe that it is nevertheless wide enough to provide a solid basis to young researchers in the field.

Among the “hot topics” that are at present vigorously debated in the literature is liquid water polymorphism. While polymorphism is a well-known phenomenon for solids, conventional wisdom has until recently asserted that a pure substance can have only one liquid phase. Evidence for liquid polymorphism and the associated liquid-liquid coexistence line was discussed during the first lecture, by H. E. Stanley. This topic is of particular importance, as the existence of an end point of the liquid-liquid coexistence line, water's hypothesized second critical point, might explain many of water's anomalous properties, such as the pronounced increase in the isothermal compressibility and the isobaric heat capacity upon cooling.

The interesting possibility that low-temperature vitreous water phases, differing in density, may be linked to similarly different liquid phases at higher temperature was reported by T. Loerting. Between these low temperature glassy phases and room temperature water, there is the strange realm of supercooled water. What is it? Under carefully controlled experimental conditions, water can remain as a liquid below the melting temperature. Under these circumstances, water is metastable with respect to ice, and it is called supercooled water. In this realm, all the oddities of water, in addition to the above-mentioned density anomaly, become more pronounced. Methods to study the structural properties of supercooled water and their differences with respect to those of ice were presented by A. K. Soper in his lecture. C. A. Angell and A. Nilsson discussed water properties in the fascinating realm of supercooled conditions, including the especially challenging region known as “no man's land”. The investigation of this metastable region, where water is too cold not to freeze upon cooling from the liquid side, and too warm not to crystallize upon heating from the vitreous state, requires new strategies, such as those presented by M. A. Ricci and R. Saykally. These are of particular relevance, as the location of the hypothesized second critical point is believed to lie in “no man's land”.

The study of the properties of water as a solvent is another important topic. Examples range from water in the atmosphere, as discussed in the lecture by T. Koop, to water at the interface of biomolecules, as addressed in the lecture by F. Mallamace. The study of water-biomolecule interactions brings us back to Paracelsus' statement and to the question of whether water is indeed a unique and universal matrix of life, or whether on the contrary it is just the one that happens to pertain to our planet. Fundamental to that question is the role that water plays in sustaining the biochemistry of the cell. It has become increasingly clear over the past two decades that water is not simply “life's solvent” but is indeed a matrix more akin to the one Paracelsus envisaged: a substance that actively engages and interacts with biomolecules in complex, subtle, and essential ways.

A reliable test for the successful outcome of an event like the one we have organized is whether in, say, 20 years, significant advances will have occurred in our understanding of water that can be traced to the ideas discussed in the Varenna school. Obviously (and unfortunately!) we have no crystal ball, but we can make a list of the required ingredients and hope for the better. This list surely includes the beauty of the location, the curiosity and interest of the students triggered by the lectures, and, last but not least, the overall atmosphere encouraging interaction, discussion, and friendship. In Varenna we had all of the above in spades.