S. A. Mao, Rainer Beck, Aritra Basu, Lerato Baidoo, Andrea Bracco, Ralf-Jürgen Dettmar, Volker Hessen, Cathy Horellou, Timea O. Kovacs, Kohei Kurahara, Yu-Qing Lou, Yik Ki Ma, Rikuto Omae, Rosita Paladino, Amit Seta, Fatemeh Tabatabaei, Theresa Wiegert

In order to understand the magnetization of galaxies and the role of magnetic fields in feedback processes that govern star formation and galaxy evolution, it is essential to have a comprehensive census of magnetic fields in and around galaxies from the nearby Universe to high redshifts. In this chapter, we outline the science goals, strategies, techniques, and observational requirements with SKA AA4 for (1) a homogeneous polarimetric survey of nearby galaxies - mapping both the diffuse polarized emission as well as producing a dense RM grid within the virial radius; (2) a survey of the interstellar magnetic fields in distant galaxies targeting strong lensing systems with polarized lensed quasars, as well as a general statistical back-illumination survey to probe the redshift evolution of magnetic fields in the CGM. These proposed observations will serve as a major step towards understanding the co-evolution of galaxies and their magnetic fields over cosmic time and provide constraints on galactic dynamo theories.