  We explore potential of current and next-generation gamma-ray telescopes for
the detection of weak magnetic fields in the intergalactic medium. We
demonstrate that using two complementary techniques, observation of extended
emission around point sources and observation of time delays in gamma-ray
flares, one would be able to probe most of the cosmologically and
astrophysically interesting part of the "magnetic field strength" vs.
"correlation length" parameter space. This implies that gamma-ray observations
with Fermi and ground-based Cherenkov telescopes will allow to (a) strongly
constrain theories of the origin of magnetic fields in galaxies and galaxy
clusters and (b) discover, constrain or rule out the existence of weak
primordial magnetic field generated at different stages of evolution of the
Early Universe.
