Short answers, pulled from the story.
Exsultate jubilate is a motet for solo voice and orchestra by Wolfgang Amadeus Mozart, catalogued as K. 165 and composed in 1773. It has four sections: an opening Allegro in F major, a secco recitative, an Andante in A major, and a closing Alleluia. Although nominally a liturgical work, it shares many features with Mozart's concert arias and uses elements of concerto form.
Mozart composed Exsultate jubilate for the castrato Venanzio Rauzzini, who had sung the role of Cecilio in Mozart's opera Lucio Silla at the Teatro Regio Ducale in Milan. The text of the motet may have been written by Rauzzini himself, though the attribution remains unconfirmed.
Exsultate jubilate received its first performance on the 17th of January 1773, at the Theatine Church in Milan. It was composed during the final weeks of the run of Lucio Silla, which ran from the 26th of December 1772 to the 25th of January 1773.
The four sections of Exsultate jubilate are an Allegro in F major, a secco recitative, an Andante in A major, and a closing Alleluia. Musicologist Stanley Sadie described the Alleluia as "a jewel of a piece with its high spirits and its wit... like no other piece of Mozart's."
The manuscripts of the two Salzburg versions of Exsultate jubilate were discovered in 1978 in St. Jakob, Wasserburg am Inn. One version was performed by Francesco Ceccarelli at the Holy Trinity Church in Salzburg on the 30th of May 1779, a Trinity Sunday, and a second version was intended for Christmas.
Exsultate jubilate has been recorded by sopranos including Arleen Auger, Carolyn Sampson, Danielle de Niese, and Julia Lezhneva, and by countertenors including Michael Maniaci, Franco Fagioli, and Aris Christofellis. Carolyn Sampson recorded it twice, in 2005 with Robert King and the King's Consort and in 2015 with Masaaki Suzuki and Bach Collegium Japan.