  We study briefly some properties of real Clifford algebras and identify them
as matrix algebras. We then show that the representation space on which
Clifford algebras act are spinors and we study in details matrix
representations. The precise structure of these matrices gives rise to the type
of spinors one is able to construct in a given space-time dimension: Majorana
or Weyl. Properties of spinors are also studied. We finally show how Clifford
algebras enable us to construct supersymmetric extensions of the Poincar\'e
algebra. A special attention to the four, ten and eleven-dimensional
space-times is given. We then study the representations of the considered
supersymmetric algebras and show that representation spaces contain an equal
number of bosons and fermions. Supersymmetry turns out to be a symmetry which
mixes non-trivially the bosons and the fermions since one multiplet contains
bosons and fermions together. We also show how supersymmetry in four and ten
dimensions are related to eleven dimensional supersymmetry by compactification
or dimensional reduction.
