Trails in Kinetic Theory : Foundational Aspects and Numerical Methods J. A. Carrillo et al. Recent Development In Kinetic Theory Of Granular Materials: Analysis And Numerical Methods R. Borsche and A. Klar Asymptotic methods for kinetic and hyperbolic evolution equations on networks Marina A. Ferreira Coagulation equations for aerosol dynamics F. Bourdin and B. Maury Multibody and macroscopic impact laws: a Convex Analysis Standpoint L. Pareschi An introduction to uncertainty quantification for kinetic equations and related problems M. Pulvirenti and S. Simonella A brief introduction to the scaling limits and effective equations in kinetic theory G. Toscani Statistical description of human addiction phenomena A. Tosin and M. Zanella Boltzmann type description with cutoff of Follow the Leader traffic models. In recent decades kinetic theory originally developed as a field of mathematical physics has emerged as one of the most prominent fields of modern mathematics. In recent years there has been an explosion of applications of kinetic theory to other areas of research such as biology and social sciences. This book collects lecture notes and recent advances in the field of kinetic theory of lecturers and speakers of the School “Trails in Kinetic Theory: Foundational Aspects and Numerical Methods” hosted at Hausdorff Institute for Mathematics (HIM) of Bonn Germany 2019 during the Junior Trimester Program “Kinetic Theory”. Focusing on fundamental questions in both theoretical and numerical aspects it also presents a broad view of related problems in socioeconomic sciences pedestrian dynamics and traffic flow management.