Answer by taking a quote from the following article:

Rudolf Joseph Lorenz Steiner (27 (or 25) February 1861 - 30 March 1925) was an Austrian philosopher, social reformer, architect and esotericist. Steiner gained initial recognition at the end of the nineteenth century as a literary critic and published philosophical works including The Philosophy of Freedom. At the beginning of the twentieth century he founded an esoteric spiritual movement, anthroposophy, with roots in German idealist philosophy and theosophy; other influences include Goethean science and Rosicrucianism. In the first, more philosophically oriented phase of this movement, Steiner attempted to find a synthesis between science and spirituality.

The Anthroposophical Society grew rapidly. Fueled by a need to find an artistic home for their yearly conferences, which included performances of plays written by Edouard Schure and Steiner, the decision was made to build a theater and organizational center. In 1913, construction began on the first Goetheanum building, in Dornach, Switzerland. The building, designed by Steiner, was built to a significant part by volunteers who offered craftsmanship or simply a will to learn new skills. Once World War I started in 1914, the Goetheanum volunteers could hear the sound of cannon fire beyond the Swiss border, but despite the war, people from all over Europe worked peaceably side by side on the building's construction.  Steiner's lecture activity expanded enormously with the end of the war. Most importantly, from 1919 on Steiner began to work with other members of the society to found numerous practical institutions and activities, including the first Waldorf school, founded that year in Stuttgart, Germany. At the same time, the Goetheanum developed as a wide-ranging cultural centre. On New Year's Eve, 1922/1923, the building burned to the ground; contemporary police reports indicate arson as the probable cause. Steiner immediately began work designing a second Goetheanum building - this time made of concrete instead of wood - which was completed in 1928, three years after his death.  At a "Foundation Meeting" for members held at the Dornach center during Christmas, 1923, Steiner spoke of laying a new Foundation Stone for the society in the hearts of his listeners. At the meeting, a new "General Anthroposophical Society" was established with a new executive board. At this meeting, Steiner also founded a School of Spiritual Science, intended as an "organ of initiative" for research and study and as "the 'soul' of the Anthroposophical Society". This School, which was led by Steiner, initially had sections for general anthroposophy, education, medicine, performing arts (eurythmy, speech, drama and music), the literary arts and humanities, mathematics, astronomy, science, and visual arts. Later sections were added for the social sciences, youth and agriculture. The School of Spiritual Science included meditative exercises given by Steiner.

When was the second one completed?
was completed in 1928, three years after his death.