Measure and integral, definitions -- Basic result on construction of a measure -- Basic result on construction of an integral -- Finitely additive theory -- From “Baire” measures to “Borel” measures, an abstract approach -- Construction of measures by approximation from outside and by approximation from inside -- On the possibility of providing a space of measures with a vague topology -- Definition and basic properties of the weak topology -- Compactness in the weak topology -- Criteria for weak convergence -- On the structure of M +(X) -- A problem related to questions of uniformity -- First solution of the ?-problem -- Second solution of the ?-problem -- Uniformity classes -- Joint continuity -- Preservation of weak convergence.