Introduction to extra dimensions

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.