The horn is a wonderful solo instrument and has a surprisingly large repertoire, whether concertos, sonatas or works for horn in chamber music.
The first horn concertos date back to the era of Bach and Handel, even if these two did not write any horn concertos. Bach does feature the horn or horns in a number of works, the first Brandenburg concerto, with two horns and ensemble, a solo part in one section of the great Mass in B minor, and several cantatas. There is an aria sung by Julius Caesar in Handel's eponymous opera (Giulio Cesare in Italian), with a prominent and difficult part for solo horn.
Mozart wrote four horn concertos and a quintet for horn and strings, plus a few fragments of other works for horn. Three of these were written for the horn player Joseph Leutgeb, a well-known musician of the time. Apparently, Mozart thought he was something of what we would call a dork, and made some funny and obscene comments about him in his manuscripts. The concertos are delightful works, and feature last movements with a hunt like character, as early horns had often been used in hunting.
Mozart's great older contemporary and friend Joseph Haydn wrote two horn concertos, one whose authenticity of authorship is uncertain. Haydn's symphony no 31, the Hunt symphony, features prominent parts for four horns.
A relatively early work of Beethoven is a sonata for horn and piano, which Beethoven premiered with the than famous Bohemian born hornist Giovanni Punto. Carl Maria von Weber (1786- 1826), best known for his colorful folkloric opera Der Freischutz (The Freeshooter ), wrote very difficult concertino for horn and orchestra , which features a cadenza in which the soloist is supposed to play chords by simultaneously humming and playing, which produces audible overtones if done correctly ! This technique was discovered in the late 18th century.
Robert Schumann (1810- 1856), was the first great composer to feature the relatively new valved horn as a solo instrument. His Konzertstuck ,or concert piece, for four horns and orchestra, from 1849, is a wonderful piece but terrifying difficult to play. The first horn part is so appallingly difficult that only the greatest horn players in orchestras would dare to attempt it.
Richard Strauss ( 1864- 1949 ), wrote two horn concertos, the first as a teenager in his native Munich, and the second many years later when he was almost 80. Strauss was the son of Franz Strauss ( 1822-1905 ), who was considered the greatest horn player of the 19th century. The elder Strauss was first horn at the Royal opera in Munich for many years, and his son grew up steeped in the sound of that instrument. Franz Strauss also wrote a horn concerto and other works. Both are very attractive works; the second is much more difficult to play. The orchestral and operatic works of Richard are filled with juicy but difficult horn parts which every horn player learns as a student and practices carefully.
The Ukrainian born Reinhold Gliere (1875- 1956 ) is best known for the Russian Sailor's dance from the Chinese flavored ballet "The Red Poppy", also wrote an entertaining horn concerto. The German Paul Hindemith (1895- 1963), and a number of other 20th centuries have also written horn concertos. This list is just the tip of the iceberg for the solo horn repertoire.
There are many excellent recordings of horn concertos and other works for this instrument with such great horn virtuosos as England's Dennis Brain (1921- 1957), Australian Barry Tuckwell (1931-), now retired, Hermann Baumann of Germany, and Peter Damm, recently retired as principal horn of the famous Dresden State orchestra, principal horn Dale Clevenger of the Chicago symphony, William Purvis of the Orpheus chamber orchestra (one of my teachers), and others.