  In these lectures we study some possible higher order (of degree greater than
two) extensions of the Poincar\'e algebra. We first give some general
properties of Lie superalgebras with some emphasis on the supersymmetric
extension of the Poincar\'e algebra or Supersymmetry. Some general features on
the so-called Wess-Zumino model (the simplest field theory invariant under
Supersymmetry) are then given. We further introduce an additional algebraic
structure called Lie algebras of order F, which naturally comprise the concepts
of ordinary Lie algebras and superalgebras. This structure enables us to define
various non-trivial extensions of the Poincar\'e algebra. These extensions are
studied more precisely in two different contexts. The first algebra we are
considering is shown to be an (infinite dimensional) higher order extension of
the Poincar\'e algebra in $(1+2)-$dimensions and turns out to induce a symmetry
which connects relativistic anyons. The second extension we are studying is
related to a specific finite dimensional Lie algebra of order three, which is a
cubic extension of the Poincar\'e algebra in $D-$space-time dimensions.
Invariant Lagrangians are constructed.
