  The aim of this talk is to provide non-experts with a brief and elementary
introduction on the field of extra dimensions. The main motivation for extra
dimensions relies on the more fundamental string theories that predict ten (or
eleven) space-time dimensions. Extra dimensions must be compactified and there
appear branes where gauge and/or gravity propagates. Compactification relates
string constants (string scale and string coupling) with four-dimensional
constants (Planck scale and gauge coupling). Only gravity can propagate in
dimensions transverse to the brane. They can be detected either by
gravitational (table-top) or by collider experiments where Kaluza-Klein
graviton production appears as missing energy. Transverse dimensions can be as
large as the sub-millimeter. Ordinary matter can also propagate in dimensions
parallel to the brane. It can give rise to bumps in the dilepton invariant mass
in hadron colliders or contribute by indirect effects to the electroweak
observables. Longitudinal dimensions can be probed at LHC up to a scale of 6.7
TeV (9 TeV) for one (two) extra dimension(s). Extra dimensions also give rise
to new theoretical ideas related to supersymmetry and electroweak breaking.
Some of these ideas are reviewed.
