  The constantly improving sensitivity of ground-based and space-borne
observatories has made possible the detection of high-energy emission (X-rays
and gamma-rays) from several thousands of extragalactic sources. Enormous
progress has been made in measuring the continuum flux enabling us to perform
imaging, spectral and timing studies. An important remaining challenge for
high-energy astronomy is measuring polarization. The capability to measure
polarization is being realized currently at X-ray energies (e.g. with IXPE),
and sensitive gamma-ray telescopes capable of measuring polarization, such as
AMEGO, AdEPT, e-ASTROGAM, etc., are being developed. These future gamma-ray
telescopes will probe the radiation mechanisms and magnetic fields of
relativistic jets from active galactic nuclei at spatial scales much smaller
than the angular resolution achieved with continuum observations of the
instrument. In this white paper, we discuss the scientific potentials of
high-energy polarimetry, especially gamma-ray polarimetry, including the
theoretical implications, and observational technology advances being made. In
particular, we will explore the primary scientific opportunities and wealth of
information expected from synergy of multi-wavelength polarimetry that will be
brought to multi-messenger astronomy.
