  An extensive group-theoretical treatment of linear relativistic field
equations on Minkowski spacetime of arbitrary dimension D>2 is presented in
these lecture notes. To start with, the one-to-one correspondence between
linear relativistic field equations and unitary representations of the isometry
group is reviewed. In turn, the method of induced representations reduces the
problem of classifying the representations of the Poincare group ISO(D-1,1) to
the classication of the representations of the stability subgroups only.
Therefore, an exhaustive treatment of the two most important classes of unitary
irreducible representations, corresponding to massive and massless particles
(the latter class decomposing in turn into the ``helicity'' and the
"infinite-spin" representations) may be performed via the well-known
representation theory of the orthogonal groups O(n) (with D-4<n<D). Finally,
covariant field equations are given for each unitary irreducible representation
of the Poincare group with non-negative mass-squared. Tachyonic representations
are also examined. All these steps are covered in many details and with
examples. The present notes also include a self-contained review of the
representation theory of the general linear and (in)homogeneous orthogonal
groups in terms of Young diagrams.
