  We study the {\em propagation of electromagnetic waves} in a spacetime devoid
of a metric but equipped with a {\em linear} electromagnetic spacetime relation
$H\sim\chi\cdot F$. Here $H$ is the electromagnetic excitation $({\cal D},{\cal
H})$ and $F$ the field strength $(E,B)$, whereas $\chi$ (36 independent
components) characterizes the electromagnetic permittivity/permeability of
spacetime. We derive analytically the corresponding Fresnel equation and show
that it is always quartic in the wave covectors. We study the `Fresnel tensor
density' ${\cal G}^{ijkl}$ as (cubic) function of $\chi$ and identify the
leading part of $\chi$ (20 components) as indispensable for light propagation.
Upon requiring electric/magnetic reciprocity of the spacetime relation, the
leading part of $\chi$ induces the {\em light cone} structure of spacetime (9
components), i.e., the spacetime metric up to a function. The possible
existence of an Abelian {\em axion} field (1 component of $\chi$) and/or of a
{\em skewon} field (15 components) and their effect on light propagation is
discussed in some detail. The newly introduced skewon field is expected to be
T-odd and related to dissipation.
