The book collects relevant contributions presented at a conference, organized in honour of Carlo Cercignani, that took place at Politecnico di Milano on May 24-28, 2021.Different research areas characterizing the scientific work of Carlo Cercignani have been considered with a particular focus on: mathematical and numerical methods for kinetic equations; kinetic modelling of gas mixtures and polyatomic gases; applications of the Boltzmann equation to electron transport, social phenomena and epidemic spread; turbulence modelling; the Einstein Classical Program; Dynamical Systems Theory.