Quantitative Biosciences establishes the quantitative principles of how living systems work across scales, drawing on classic and modern discoveries to present a case study approach that links mechanisms, models, and measurements. Each case study is organised around a central question in the life sciences: Are mutations dependent on selection? How do cells respond to fluctuating signals in the environment? How do organisms move in flocks given local sensing? How does the size of an epidemic depend on its initial speed of spread? Each question provides the basis for introducing landmark advances in the life sciences while teaching students - whether from the life sciences, physics, computational sciences, engineering, or mathematics - how to reason quantitatively about living systems given uncertainty.