This book focuses on the interplay between Eulerian and Lagrangian conservation laws for
systems that admit physical motivation and originate from continuum mechanics. Ultimately it
highlights what is specific to and beneficial in the Lagrangian approach and its numerical
methods. The two first chapters present a selection of well-known features of conservation laws
and prepare readers for the subsequent chapters which are dedicated to the analysis and
discretization of Lagrangian systems. The text is at the frontier of applied mathematics and
scientific computing and appeals to students and researchers interested in Lagrangian-based
computational fluid dynamics. It also serves as an introduction to the recent corner-based
Lagrangian finite volume techniques.
