D-brane physics at low energies

In how many dimensions do we live? Could they be more than the four we are aware of? If so, why don't we see the other dimensions? Is there a way to detect them? While the possibility of extra-dimensions has been considered by physicists for long time, a compelling reason for their existence has arisen with string theory. It seems that a quantum theory of gravity requires that we live in more than four dimensions, probably in ten or eleven dimensions. The remaining (space-like) six or seven dimensions are hidden to us: observed particles do not propagate in them. The theory does not tell us yet why four and only four have been accessible to us. However, it predicts that this is only a low-energy effect: With increasing energy, particles which propagate in a higher dimensional space could be produced. What is the value of the needed high energy scale? could it be just close by, at reach of near future experiments? Another scale which appears in our attempts to answer the previous questions is related to the extended nature of fundamental objects. It is the scale at which internal degrees of freedom are excited. In string theory this scale M, is related to the string tension and sets the mass of the first heavy oscillation mode. The pointlike behavior of known particles as observed at present colliders allows to conclude that M has to be higher than a few hundred GeV. It is the aim of these lectures as to provide a short summary of the present status of research on extra-dimensions and string-like sub-structure of matter. (22 refs).