This piece of music by Agustín Barrios Mangoré [1885-1944] is from a work named La Catedral. It consists of three pieces: Preludio Saudade, Andante Religioso and Allegro Solemne. It is originally a piece for the guitar.
Additional information from imslp.org: At first La Catedral was composed 1921 in Montevideo (Uruguay), subtitled "Dístico sacro" with just the 2 pieces "Andante religioso" + "Allegro solemne". The "Preludio (Saudade)" was composed in Habana (Cuba) 1938 and added as the 1st piece of La Catedral in 1939.
Pictures of settings concerning the sound of the music in the video:
Musical Pieces 
