A geodesic dome is a hemispherical thin-shell structure (lattice-shell) based on a geodesic polyhedron. The triangular elements of the dome are structurally rigid and distribute the structural stress throughout the structure, making geodesic domes able to withstand very heavy loads for their size. 

The first dome that could be called "geodesic" in every respect was designed after World War I by Walther Bauersfeld, chief engineer of the Carl Zeiss optical company, for a planetarium to house his planetarium projector. A first, small dome was patented, constructed by the firm of Dykerhoff and Wydmann on the roof of the Zeiss plant in Jena, Germany. A larger dome, called "The Wonder of Jena", opened to the public in July 1926. Some 20 years later, R. Buckminster Fuller named the dome "geodesic" from field experiments with artist Kenneth Snelson at Black Mountain College in 1948 and 1949. Although Fuller was not the original inventor, he is credited with the U.S. popularization of the idea for which he received U.S. patent 2,682,235 29 June 1954. 

The geodesic dome appealed to Fuller because it was extremely strong for its weight, its "omnitriangulated" surface provided an inherently stable structure, and because a sphere encloses the greatest volume for the least surface area.
Who made the first geodesic dome?
The first dome that could be called "geodesic" in every respect was designed after World War I by Walther Bauersfeld,