The Respiratory System in Equations Introduction Lumped models The lung as a resistive tree Computing velocity fields Gas exchanges The lung as an infinite tree Data Solutions to exercises Complements Glossary. The book proposes an introduction to the mathematical modeling of the respiratory system. A detailed introduction on the physiological aspects makes it accessible to a large audience without any prior knowledge on the lung. Different levels of description are proposed from the lumped models with a small number of parameters (Ordinary Differential Equations) up to infinite dimensional models based on Partial Differential Equations. Besides these two types of differential equations two chapters are dedicated to resistive networks and to the way they can be used to investigate the dependence of the resistance of the lung upon geometrical characteristics. The theoretical analysis of the various models is provided together with state of the art techniques to compute approximate solutions allowing comparisons with experimental measurements. The book contains several exercises most of which are accessible to advanced undergraduate students.