It is being discussed if the surname should be just "Mendelssohn" (common in English) or "Mendelssohn Bartholdy" (common in German) (1,2,3,4).
Exhaustive list of works (in French): http://infopuq.uquebec.ca/~uss1010/catal/mendelssohn/menf.html
Jakob Ludwig Felix Mendelssohn Bartholdy (German: [ˈjaːkɔp ˈluːtvɪç ˈfeːlɪks ˈmɛndl̩szoːn baʁˈtɔldi]; 3 February 1809 – 4 November 1847(1847-11-04) (aged 38)), born and widely known as Felix Mendelssohn, was a German composer, pianist, organist and conductor of the early Romantic period.
A grandson of the philosopher Moses Mendelssohn, Felix Mendelssohn was born into a prominent Jewish family. He was brought up without religion until the age of seven, when he was baptised as a Reformed Christian. Mendelssohn was recognised early as a musical prodigy, but his parents were cautious and did not seek to capitalise on his talent.
Mendelssohn enjoyed early success in Germany, where he also revived interest in the music of Johann Sebastian Bach, and in his travels throughout Europe. He was particularly well received in Britain as a composer, conductor and soloist, and his ten visits there – during which many of his major works were premiered – form an important part of his adult career. His essentially conservative musical tastes, however, set him apart from many of his more adventurous musical contemporaries such as Franz Liszt, Richard Wagner and Hector Berlioz. The Leipzig Conservatoire (now the University of Music and Theatre Leipzig), which he founded, became a bastion of this anti-radical outlook.
Mendelssohn wrote symphonies, concerti, oratorios, piano music and chamber music. His best-known works include his Overture and incidental music for A Midsummer Night's Dream, the Italian Symphony, the Scottish Symphony, the overture The Hebrides, his mature Violin Concerto, and his String Octet. His Songs Without Words are his most famous solo piano compositions. After a long period of relative denigration due to changing musical tastes and antisemitism in the late 19th and early 20th centuries, his creative originality has now been recognised and re-evaluated. He is now among the most popular composers of the Romantic era.