A complex hypersurface $D$ in ${ℂ}^n$ is a linear free divisor (LFD) if its module of logarithmic vector fields has a global basis of linear vector fields. We classify all LFDs for $n$ at most $4$.By analogy with Grothendieck’s comparison theorem, we say that the global logarithmic comparison theorem (GLCT) holds for $D$ if the complex of global logarithmic differential forms computes the complex cohomology of ${ℂ}^n\setminus D$. We develop a general criterion for the GLCT for LFDs and prove that it is fulfilled whenever the...