  The Maxwell equations are formulated in a generally covariant and metric-free
way in 1+3 and subsequently in 4 dimensions. For this purpose, we use the
excitations $\cal D$, $\cal H$ and the field strengths $E,B$. A local and
linear constitutive law between excitations and field strengths is assumed,
with a constitutive tensor $\chi^{ijkl}=-\chi^{jikl}=-\chi^{ijlk}$ of 36
components. The properties of this tensor are discussed. In particular, we
address the validity of the Post constraint, a subject that is very much under
discussion. In this connection, the Tellegen gyrator, the axion field, and the
``perfect electromagnetic conductor'' of Lindell & Sihvola are compared with
each other.
