Short answers, pulled from the story.
Telemachus is the son of Odysseus and Penelope who grows up without knowing his father because Odysseus left when Telemachus was still an infant. The name Τηλέμαχος means far from battle or fighting from afar like a bowman does.
Telemachus joins his father in slaughtering every man who had invaded their home after Odysseus drops his disguise as a beggar. They gather weapons hidden beneath the floorboards of the great hall before the suitors fail to string the bow.
Telemachus boards a ship bound for Pylos where King Nestor sits among elders who remember the Trojan War. He then sails to Sparta where Menelaus and Helen speak of how Odysseus was last seen stranded on Ogygia, an island ruled by Circe.
Some versions say he married Circe the goddess who once turned men into beasts while other accounts claim he wed Nausicaa daughter of King Alcinous. A different tradition states Polycaste Nestor's daughter became his wife instead.
André Cardinal Destouches composed an opera titled Télémaque in 1714 based on Fénelon's novel Les Aventures de Télémaque. Alessandro Scarlatti followed with Telemaco in 1718 while Gluck presented Telemaco ossia L'isola di Circe in 1765.