We theoretically study various fluid mathematical models in the soft matter realm. Some of these are of biological interest some others are interesting from the point of view of the realization and engineering of new materials. These fluids are made of particles of dimensions ranging from nanometers to micrometers and obey generally to Boltzmann statistics. These colloidal particles may have complex pair-potentials which give rise to peculiar self-assembly properties. Another interesting issue is the determination of the surface properties (like the interface between two different phases, membranes formed by amphiphilic surfactant molecules such as lipids and their fluctuations, or plasma confined in low dimensionality) of these complex fluids.

Recently developed laboratory techniques and theoretical methods have enabled the manufacture or the computer simulation of matter exhibiting new types of order. Some of the most spectacular advances made in this direction have been in material science, where the pace of technological advance is such that materials can be grown atom by atom or, on the other extreme, on the scale of micrometers using colloidal particles as the building blocks.

Physicists are now able to "order up" totally new material structures, on scales ranging from nano to mesoscopic dimensions and then proceed to explore their structural and thermodynamic properties. As a result a whole new field of quantum physics has appeared, the physics of nano-structures, where new phenomena, many with obvious technological applications, are being discovered almost daily (report on Nanotechnologies in Venice). New technological advances have also allowed physicists to manipulate colloids in such a way that their effective interactions can be controlled in detail. In many cases these interactions differ in fundamental ways from atomic interactions, paving the way for the assembly of new structures that cannot be found in the realm of atomic materials.

Some interesting unresolved problems for example are the vitrification of hard-spheres and the determination of the phase diagram of strongly size asymmetric binary hard-sphere mixtures.