The Hubble UV Legacy Library of Young Stars as Essential Standards (ULLYSES) Director’s Discretionary Program of low-mass pre-main-sequence stars, coupled with forthcoming data from Atacama Large Millimeter/submillimeter Array and James Webb Space Telescope, will provide the foundation to revolutionize our understanding of the relationship between young stars and their protoplanetary disks. A comprehensive evaluation of the physics of disk evolution and planet formation requires understanding the intricate relationships between mass accretion, mass outflow, and disk structure. Here we describe the Outflows and Disks around Young Stars: Synergies for the Exploration of ULLYSES Spectra (ODYSSEUS) Survey and present initial results of the classical T Tauri Star CVSO 109 in Orion OB1b as a demonstration of the science that will result from the survey. ODYSSEUS will analyze the ULLYSES spectral database, ensuring a uniform and systematic approach in order to (1) measure how the accretion flow depends on the accretion rate and magnetic structures, (2) determine where winds and jets are launched and how mass-loss rates compare with accretion, and (3) establish the influence of FUV radiation on the chemistry of the warm inner regions of planet-forming disks. ODYSSEUS will also acquire and provide contemporaneous observations at X-ray, optical, near-IR, and millimeter wavelengths to enhance the impact of the ULLYSES data. Our goal is to provide a consistent framework to accurately measure the level and evolution of mass accretion in protoplanetary disks, the properties and magnitudes of inner-disk mass loss, and the influence of UV radiation fields that determine ionization levels and drive disk chemistry.