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Astrophysical ages and time scales provide the basis for a host of studies in astronomy, ranging from planetary and star formation, to the abundances of the elements, cosmochronology, and the concordance of cosmological parameters. Indeed, the determination of the ages of the Earth, Sun, Galaxy, and Universe has occupied a primary role in biology, geology, physics, and astronomy in the modern era. In addition to the historical importance of astrophysical ages, observations over the past decade from a host of new x-ray, optical, infrared, and radio telescopes and theoretical advances in physics, chemistry, and biology have changed the landscape of the topic. For instance, helioseismology has critically refined our understanding of stellar structure, and technological revolutions in ground- and space-based multi-messenger astronomy (e.g., LIGO, LISA, JWST, Euclid, Roman, Rubin) have opened, or should soon reveal, critical windows on star formation processes, galaxies at large look-back times, gravitational physics, and the earliest days of structure formation. The results of these myriad observational and theoretical advances are now becoming precise enough that conflicts have arisen, such as the Hubble tension, the cosmological lithium problem, the lack of an age–metallicity relation in the Galactic disk (from asteroseismology), the cause for fast radio bursts, and more. All fields of astronomy advances hinge upon greater precision in astrophysical ages. We are organizing a conference to determine the state of the art in measuring astrophysical ages and time scales, discuss conflicts in current astrophysical ages and time scales from solar system formation timescales through the age of the Universe, and assess where greater age precision is most needed. Connecting time scales from different subfields of astrophysics will also be emphasized. From all perceived conflicts and contradictions between ages obtained via different techniques and across various astronomical fields, we will map out promising lines of inquiry for resolving these differences.