This paper, translated from Edward Purcell's famous lecture notes "Life at low Reynolds number," discusses the unique world of low Reynolds number phenomena, which is dominated by organisms that move through fluids with minimal inertia. The author, Edward Purcell, introduces the concept of low Reynolds numbers and their significance, particularly in the context of fluid dynamics. He explains that in low Reynolds number environments, such as the movement of microorganisms in glycerol, the effects of viscosity dominate over inertia. This leads to interesting behaviors, such as the inability of bacteria to swim in a straight line due to their small Reynolds numbers. Purcell highlights the work of Howard Berg, who studied the swimming patterns of E. coli bacteria. Through detailed observations and experiments, Berg discovered that E. coli does not swim by wiggling its flagellum but by rotating it, much like a corkscrew. This discovery challenges traditional understanding and reveals a complex mechanism for movement in low Reynolds number fluids. The paper also explores theoretical models and experiments to understand how such organisms can move efficiently in their environment. Purcell discusses the concept of a "propulsion matrix" and how it relates to the efficiency of movement. Despite the simplicity of the models, the actual fluid dynamics are more complex than expected, leading to unexpected results and highlighting the challenges in understanding low Reynolds number phenomena. Overall, the paper emphasizes the importance of low Reynolds number physics in understanding the behavior of microorganisms and the unique solutions they develop to navigate their environment.This paper, translated from Edward Purcell's famous lecture notes "Life at low Reynolds number," discusses the unique world of low Reynolds number phenomena, which is dominated by organisms that move through fluids with minimal inertia. The author, Edward Purcell, introduces the concept of low Reynolds numbers and their significance, particularly in the context of fluid dynamics. He explains that in low Reynolds number environments, such as the movement of microorganisms in glycerol, the effects of viscosity dominate over inertia. This leads to interesting behaviors, such as the inability of bacteria to swim in a straight line due to their small Reynolds numbers. Purcell highlights the work of Howard Berg, who studied the swimming patterns of E. coli bacteria. Through detailed observations and experiments, Berg discovered that E. coli does not swim by wiggling its flagellum but by rotating it, much like a corkscrew. This discovery challenges traditional understanding and reveals a complex mechanism for movement in low Reynolds number fluids. The paper also explores theoretical models and experiments to understand how such organisms can move efficiently in their environment. Purcell discusses the concept of a "propulsion matrix" and how it relates to the efficiency of movement. Despite the simplicity of the models, the actual fluid dynamics are more complex than expected, leading to unexpected results and highlighting the challenges in understanding low Reynolds number phenomena. Overall, the paper emphasizes the importance of low Reynolds number physics in understanding the behavior of microorganisms and the unique solutions they develop to navigate their environment.