The book is dedicated to the Lebesgue integral. A construction based on integral sums is considered at a fairly high level of abstraction. A measure, a generalized measure and some specific measures are preliminarily introduced and studied in detail: Lebesgue measure, Lebesgue-Stiles measure, probabilistic measure. Measurable mappings and questions related to sequence and series convergence of measurable mappings are then examined. The Lebesgue integral is considered by a generalized measure.