A pedagogical review of the mathematical modelling in fluid dynamics necessary to understand the motility of most microorganisms on Earth.

Eric Lauga is Professor of Applied Mathematics at the University of Cambridge and a Fellow of Trinity College, Cambridge. He is the author, or co-author, of over 170 publications in the field of fluid mechanics, biophysics and soft matter. He is a recipient of a CAREER Award from the US National Science Foundation (2008), and of three awards from the American Physical Society: the Andreas Acrivos Dissertation Award in Fluid Dynamics (2006), the François Frenkiel Award for Fluid Mechanics (2015) and the Early Career Award for Soft Matter Research (2018). Lauga is a Fellow of the American Physical Society.

Part I. Fundamentals: 1. Biological background; 2. The fluid dynamics of microscopic locomotion; 3. The waving sheet model; 4. The squirmer model; Part II. Cellular locomotion: 5. Flagella and the physics of viscous propulsion; 6. Hydrodynamics of slender filaments; 7. Waving of eukaryotic flagella; 8. Rotation of bacterial flagellar filaments; 9. Flows and stresses induced by cells; Part III. Interactions: 10. Swimming cells in flows; 11. Self-propulsion and surfaces; 12. Hydrodynamic synchronisation; 13. Diffusion and noisy swimming; 14. Hydrodynamics of collective locomotion; 15. Locomotion and transport in complex fluids; References; Index.