The process of spreading an aerosol cloud formed by a human cough was studied. Measurements were carried out on an experimental installation with three video cameras recording the process of spreading an aerosol cloud in three planes. The movement of the aerosol was visualized by scattering light on the smoke particles mixed into the aerosol cloud. The absolute values of the cloud’s velocity were determined using an anemometer. The dependence of the cloud’s propagation distance on time was determined from video frames. The dependence of the cloud’s volume on time was calculated from video frames for three planes. The graphs show the dependence of the cloud’s propagation distance and volume on time for a two-second interval. The volume of the cloud increases within 0.5 s. after release. The volume reaches its maximum (0.5 m3) within 1.2 s. Oscillations of the aerosol cloud volume have been detected. The occurrence of oscillations is explained by the influence of air flow turbulence. The diffusion theory for an aerosol cloud is considered. The solutions of the diffusion equation for an aerosol spherical and cylindrical cloud are given. The obtained data can be used to create models of virus spread in indoor spaces, develop measures to prevent the spread of infections, and design ventilation systems.