Elrond Peredhel: the master of Imladris, called Half-elven...he was Arwen's father. He was one of the twin sons of Elwing and Eärendil, who captains the ship that sails into the night sky every evening with the Silmaril, the light of the evening star, bound upon his brow.
Elrond and his twin brother Elros were separated from their parents during the sack of the Havens of Sirion and taken captive by the sons of Fëanor, however Maglor, one of afforementioned sons, took pity upon them and let them go. They were both raised by Maglor.
After the War of Wrath, the war that ended the First Age and changed the world, Elrond was offered the same choice that his daughter made: to be counted amongst Men or Elves. Elrond, of course, chose to be considered one of elven-kind, while his brother Elros chose the path of Men. Considering the bond between twins, this must have been very difficult for both the brothers. Elros became the first king of Númenor, and Elrond remained in Lindon with his liege, High King of the Elves, Erenion Gil-Galad, the bearer of the Elven Ring of Air, Vilya. He was later to become Gil-Galad's herald. After Eriador, in the far north-west of Middle-earth, was sacked by Sauron, Elrond founded the haven of Imladris deep in one of the valleys there, and it became the place he called home. When he did so, Gil-Galad entrusted Vilya to him, and Rivendell prospered with the help of the power of the Ring of Sapphire.
At the end of the Second Age, Elrond marched with Gil-Galad and Elendil, the King of the Númenoreans, in the Last Alliance against the evil of Sauron. Tragically, Gil-Galad perished in the Siege of Barad-Dûr, and left Elrond as, more or less, the High King of the Elves. The allied armies returned home, victorious against all possible hope (or so they thought...), and not long after, Elrond met a very special person indeed...
Elrond was, without a doubt, one of the most important elves in the history of Middle-earth. An interesting fact: Elros' only daughter's name, Tindómiel, means virtually the same thing as Undómiel. Was Arwen's second name a subtle nod to Elrond's brother and the niece that Elrond never knew, by chance?