Spin and Clifford algebras, an introduction

40 pages ; published version with slight modifications for on-line reading (Ed. UNAM-FQ 2002, México)International audienceIn this short pedagogical presentation, we introduce the spin groups and the spinors from the point of view of group theory. We also present, independently, the construction of the low dimensional Clifford algebras. And we establish the link between the two approaches. Finally, we give some notions of the generalisations to arbitrary spacetimes, by the introduction of the spin and spinor bundles