Short answers, pulled from the story.
Telemachus is the son of Odysseus and Penelope in Greek mythology. He is a central character in Homer's Odyssey, where he grows up during his father's twenty-year absence and eventually reunites with Odysseus to defeat the suitors who had occupied their home at Ithaca.
The name Telemachus means "far from battle" in Greek, or perhaps "fighting from afar," in the manner of a bowman.
The Telemachy is the traditional name for the first four books of the Odyssey, which follow Telemachus as he searches for news of his missing father. Guided by Athena, he travels to Pylos and Sparta, where Menelaus tells him that Odysseus was last seen stranded on the island of Ogygia.
Odysseus signals Telemachus to stop during Penelope's bow contest so that he himself can take over and reveal his identity. Telemachus had nearly succeeded on his fourth attempt at stringing the bow before Odysseus intervened.
In the Telegony, a short two-book epic poem set after the Odyssey, Odysseus is accidentally killed by Telegonus, his unknown son by the goddess Circe. After Odysseus's death, Telemachus travels to the island of Aeaea with Telegonus and Penelope, where he marries Circe.
Several eighteenth-century operas drew from François Fénelon's novel about Telemachus. The most notable include André Cardinal Destouches's Télémaque (1714), Alessandro Scarlatti's Telemaco (1718), Gluck's Telemaco, ossia L'isola di Circe (1765), and Giuseppe Gazzaniga's Gli errori di Telemaco (1776). Simon Mayr and Fernando Sor each released a Telemaco nell'isola di Calipso in 1797.