Explore the classical and modern theories of flows of vector fields in this comprehensive analysis seminar lecture. Delve into the textbook examples, classical theory, and modern approaches presented by Camillo DeLellis, Faculty and IBM von Neumann Professor at the Institute for Advanced Study's School of Mathematics. Examine key concepts such as the DiPerna-Lions approach, commutator estimates, and Ambrosio's superposition principle. Investigate well-posedness "almost everywhere" and linearity in the context of vector field flows. Gain insights into the work of Jabin, Caravenna-Crippa, and their contributions to a.e. uniqueness in this advanced mathematical exploration.