Aldarion and Erendis: The Mariner's Wife is the whole title of the second chapter of Unfinished Tales, in Part 2. It mainly concerns the first Ship-king of Númenor, Tar-Aldarion, and his wife, and how they differed. J.R.R. Tolkien composed this tale's final form no earlier than 1965. 
At the beginning of the chapter, Aldarion's father Tar-Meneldur is described, as a rightful king devoted to the Island of Númenor, but whose true passion was the study of the stars. He had two daughters and one son, named Anardil, who would be known among the Kings of Númenor as Tar-Aldarion.
Through time, disagreement arose between Aldarion and his father, concerning the Sea, for Aldarion loved it ever since he was a child. His first odyssey towards Middle-earth was made in the year SA 725, under the guidance of Vëantur, his own grandfather, and it was during that journey, upon his ship Númerrámar, that he befriended Elves Cirdan and Ereinion (Gil-galad).
More sea voyages followed afterwards, against the wish of his father, and inbetween them, he founded the Guild of Venturers. In the hundredth year of his life, he was proclaimed heir to the throne, and at the celebration of this event he met Erendis, daughter of Beregar. Though she seemed beautiful to him, Aldarion did not pursue her until later on, as he continued to follow the marine life he much loved.
When Aldarion finally courted her, it was Erendis who avoided the union, for she did not want to share Aldarion with the sea. Only after many years they were engaged, and even more passed until they were married in the year SA 870. While being husband and wife, they did not manage to reconcile their differences. A few years after their only child was born, named Ancalimë, Aldarion continued his explorations in Middle-earth. Erendis grew bitter of the perpetual waiting, until finally she left their home in Armenelos, taking their young daughter with her into the heart of Emerië.
Upon his return, Aldarion found his home locked and his father even more cold towards him. It was the same with his wife, when he pursued her to her new home. But here the tale takes an unexpected turn, as it is revealed in a letter Gil-galad wrote towards King Meneldur that Aldarion did not leave his home out of selfishness, but rather his voyages were caused by the threat from Sauron, which he had long seen and tried to prevent by building the outpost Vinyalondë at the mouth of the Gwathló river in Middle-earth. Tar-Meneldur, realizing that he did not share the visionary mind of his son, nor his capacity to face upcoming events, announced his abdication and proclaimed Aldarion as the succeeding King of Númenor.