A kinetic theory of vapor nucleation on insoluble wettable condensation nuclei is constructed. Depending on the initial parameters of a theory that determines the properties of a liquid, vapor, substance comprising the solid wettabl.e nucleus, and boundary layers and characterizes the sizes of condensation nuclei; their initial number in the vapor-gas medium; and the rate of the external creation of a metastable state in vapor, all basic kinetic characteristics of nucleation (such as the number of supercritical droplets emerging in nucleation, the time of the beginning and the duration of the emergence of supercritical droplets, and the width of the spectrum of supercritical droplet sizes) are determined in the analytical form. Characteristic cases of free-molecular and diffusion regimes of the growth of supercritical droplets are analyzed. The quantitative criterion indicating the nature of the termination of the nucleation of supercritical droplets is disclosed: whether it is caused by the absorption of vapor by supercritical droplets or by the depletion of the supply of condensation nuclei due to the formation of supercritical droplets on these nuclei. Data of numerical calculation are reported which demonstrate the ability of the kinetic theory to draw interesting practical predictions within a wide range of the values of the initial parameters of the theory. It is shown how the polydispersity of insoluble wettable condensation nuclei can be taken into account in the theory.