Topological Data Analysis (TDA) is a research area at the intersection of Algebra, Topology, Geometry, Statistics and Machine Learning. While methods from TDA have been applied successfully to data from a variety of domains — from financial mathematics, to materials science, climate science, biomedical imaging, or social science —, there has been less work done on studying in a principled way how such methods can be applied to data that changes dynamically over time. The goal of this workshop is to bring together experts in TDA with experts in application domains in which time-varying data is particularly prevalent. Examples include time series in climate modelling and financial mathematics, as well as dynamic networks in epidemiology and social science modelling.