This volume presents research and expository articles by the participants of the 25th Arkansas Spring Lecture Series on Recent Progress in the Study of Harmonic Measure from a Geometric and Analytic Point of View held at the University of Arkansas, USA. Papers in this volume provide presentations of the problems that are at the forefront of harmonic analysis and partial differential equations. The following topics are featured: the solution of the Kato conjecture, the two bricks problem, new results on Cauchy integrals on non-smooth curves, the Neumann problem for sub-Laplacians, and a...