This paper presents a mathematical theory of the coagulation kinetics of colloidal solutions, developed by M. von Smoluchowski. The author acknowledges the limitations of previous qualitative studies and the difficulty in deriving clear laws from empirical data. He proposes a theoretical framework based on the assumption that coagulation occurs due to the attraction between colloidal particles, which is influenced by the electric double layer. The theory is tested against experimental data from Zsigmondys studies on gold colloidal solutions, where coagulation was observed under different electrolyte concentrations. The mathematical model describes the coagulation process as a function of the diffusion coefficient, the radius of the attraction sphere, and the initial particle concentration. The theory is validated by comparing the predicted particle counts with experimental measurements, showing a good agreement. The paper also discusses the limitations of the theory, such as the difficulty in measuring the exact "coagulation measure" and the complexity of the physical processes involved. The theory is extended to slow coagulation, where the attraction forces are weakened due to partial decharging of the double layer. The mathematical formulation is shown to be applicable to both rapid and slow coagulation, with the key parameter being the attraction sphere radius. The theory is compared with experimental data, and it is concluded that the diffusion theory of coagulation is consistent with the observed phenomena.This paper presents a mathematical theory of the coagulation kinetics of colloidal solutions, developed by M. von Smoluchowski. The author acknowledges the limitations of previous qualitative studies and the difficulty in deriving clear laws from empirical data. He proposes a theoretical framework based on the assumption that coagulation occurs due to the attraction between colloidal particles, which is influenced by the electric double layer. The theory is tested against experimental data from Zsigmondys studies on gold colloidal solutions, where coagulation was observed under different electrolyte concentrations. The mathematical model describes the coagulation process as a function of the diffusion coefficient, the radius of the attraction sphere, and the initial particle concentration. The theory is validated by comparing the predicted particle counts with experimental measurements, showing a good agreement. The paper also discusses the limitations of the theory, such as the difficulty in measuring the exact "coagulation measure" and the complexity of the physical processes involved. The theory is extended to slow coagulation, where the attraction forces are weakened due to partial decharging of the double layer. The mathematical formulation is shown to be applicable to both rapid and slow coagulation, with the key parameter being the attraction sphere radius. The theory is compared with experimental data, and it is concluded that the diffusion theory of coagulation is consistent with the observed phenomena.