The two great works of the celebrated French mathematician Henri Lebesgue (1875-1941), Lecons sur l'integration et la recherche des fonctions primitives professees au College de France (1904) and Lecons sur les series trigonometriques professees au College de France (1906) arose from lecture courses he gave at the College de France while holding a teaching post at the University of Rennes. In 1901 Lebesgue formulated measure theory; and in 1902 his new definition of the definite integral, which generalised the Riemann integral, revolutionised integral calculus and greatly expanded the scope of Fourier analysis. The Lebesgue integral is regarded as one of the major achievements in modern real analysis, and remains central to the study of mathematics today. Both of Lebesgue's books are reissued in this series.