Homer (Ancient Greek: Ὅμηρος [hómɛːros], Hómēros) is best known as the author of the Iliad and the Odyssey. He was believed by the ancient Greeks to have been the first and greatest of the epic poets. Author of the first known literature of Europe, he is central to the Western canon. When he lived, as well as whether he lived at all, is unknown."
Source : Wikipedia
More info here at the University of Cincinnati
Observation : More detail needed. Someone obviously composed the texts, so the question might be better phrased along the lines of "Who wrote the texts attributed to Homer?"
Also see : The Trojan Warsplugin-autotooltip__plain plugin-autotooltip_bigThe Trojan Wars
"The ancient Greeks believed that Troy was located near the Dardanelles and that the Trojan War was a historical event of the 13th or 12th century BC, but by the mid-19th century AD, both the war and the city were widely seen as non-historical. In 1868, however, the German archaeologist Heinrich Schliemann met Frank Calvert, who convinced Schliemann that Troy was a real city at what is now Hisarlik in Turkey. On the basis of excavations conducted by Schliemann and others, this …