B. M. Gaensler, G. H. Heald, N. M. McClure-Griffiths, C. S. Anderson, C. L. Van Eck, J. L. West, A. J. M. Thomson, J. P. Leahy, L. Rudnick, Y. K. Ma, Takuya Akahori, G. Gürkan, T. L. Landecker, S. A. Mao, S. P. O'Sullivan, W. Raja, X. Sun, T. Vernstrom, Lerato Baidoo, Ettore Carretti, A. R. Taylor, A. G. Willis, Erik Osinga, J. D. Livingston, E. L. Alexander, David Alonso-López, A. D. Amaral, T. An, Andrea Bracco, S. Bradbury, Marcus Brüggen, Chakali Eswaraiah, Torsten Enßlin, T. J. Galvin, Marijke Haverkorn, A. M. Hopkins, Sebastian Hutschenreuter, Shinsuke Ideguchi, S. Jaswanth, S. Lyla Jung, J. F. Kaczmarek, Roland Kothes, Sanja Lazarević, Denis Leahy, Francesca Loi, Joshua R. Marvil, Ray Norris, Ayush Pandhi, Jason M. Price, C. J. Riseley, P. Ryder, Amit Seta, Vasundhara Shaw, A. X. Shen, C. Sobey, J. Stil, Chiara Stuardi, Gupta Upasana, Shannon Vanderwoude, Velibor Velović

The Australian SKA Pathfinder (ASKAP) offers powerful new capabilities for studying the polarised and magnetised Universe at radio wavelengths. In this paper, we introduce the Polarisation Sky Survey of the Universe's Magnetism (POSSUM), a groundbreaking survey with three primary objectives: (1) to create a comprehensive Faraday rotation measure (RM) grid of up to one million compact extragalactic sources across the southern ~50 per cent of the sky (20,630 deg$^2$); (2) to map the intrinsic polarisation and RM properties of a wide range of discrete extragalactic and Galactic objects over the same area; and (3) to contribute interferometric data with excellent surface brightness sensitivity, which can be combined with single-dish data to study the diffuse Galactic interstellar medium. Observations for the full POSSUM survey commenced in May 2023 and are expected to conclude by mid-2028. POSSUM will achieve an RM grid density of around 30-50 RMs per square degree with a median measurement uncertainty of ~1 rad m$^{-2}$. The survey operates primarily over a frequency range of 800-1088 MHz, with an angular resolution of 20'' and a typical RMS sensitivity in Stokes $Q$ or $U$ of 18 $\mu$Jy beam$^{-1}$. Additionally, the survey will be supplemented by similar observations covering 1296-1440 MHz over 38 per cent of the sky. POSSUM will enable the discovery and detailed investigation of magnetised phenomena in a wide range of cosmic environments, as well as the interplay between these components. This paper reviews the current science case developed by the POSSUM Collaboration and provides an overview of POSSUM's observations, data processing, outputs, and its complementarity with other radio and multi-wavelength surveys, including future work with the SKA. [Abstract abridged]