This thesis work presents the requirements and criteria for design and constructs the first SYSTEM FOR POWER GENERATION AND STORAGE OF ATMOSPHERIC ELECTRICITY based on the phenomenon of the corona current. All experiments and criteria were realized for the atmospheric conditions of Bogota-Colombia. The thesis work was performed under the hypothesis that a corona source composed by a corona electrode immersed down a natural electric field on thunderstorm conditions can provides an important corona current that can charge energy storage elements. Before design the system for power generation and storage of atmospheric electricity, the physics of the corona current was studied collecting previous works of the great authors at the beginning of the century XX as Peek (1920), Large and Pierce (1956), Rao and Bhattacharya (1966), Chapman (1970), Nasser (1971), Raizer (1987), at the end of century XX and beginning of century XI Cooray, Risk, Roman, Becerra, D’Alessandro, Arevalo, the works realized by the Electromagnetic Compatibility Research Group of the Universidad Nacional de Colombia EMC-UNC, and others. This thesis work presents laboratory experiments, results and models and simulations for describing the physics of the corona current. A measuring system of corona current was constructed and electric field sensor and professional weather station were implemented. With the measuring systems, 22 thunderstorms in Bogota-Colombia were registered. Using the 22 thunderstorms registered an algorithm prediction for thunderstorms was proposed, additional, with the results an analysis of the behavior of the corona current, electric field, pressure, temperature, humidity and wind speed were realized under thunderstorm conditions. Finally, the thesis work presents a complete description and design for constructing a corona tower for storage of atmospheric electricity and the recommendations for built a plant for power generation using corona towers.