Akallabêth is the fourth part of The Silmarillion, as edited by Christopher Tolkien (1977).
It is a relatively short (about thirty pages long) summary of the Númenor narrative of J. R. R. Tolkien's legendarium. Númenor is the name of the island which is cataclysmically destroyed in Tolkien's variant of the Atlantis legend.
In Tolkien's invented language Quenya, Atalantë means "(the) Downfallen".Akallabêth itself is the equivalent of Atalantë in Adûnaic, i.e. the language spoken in Númenor before its destruction.
Akallabêth is the story of the destruction of the Kingdom of Númenor, written by Elendil. After the downfall of the Dark Lord Morgoth at the end of the First Age (which is described in the Quenta Silmarillion) the Edain, those Men who had aided the Elves in their war against the Dark Lord were given Númenor, a new small continent of their own, free from the evil and sadness of Middle-earth. It was located in the middle of the Great Ocean, between the western shores of Middle-earth, and the eastern shores of Aman, where the Valar lived.
As they entered Númenor, Men were forbidden to set sail towards Aman. For 2500 years Númenor grew in might, with Númenórean ships sailing the seas and establishing remote colonies in Middle-earth. During that time, the Elves of Middle-earth were engaged in a bitter fight with Morgoth's former servant Sauron, who had become the second Dark Lord. The Men of Númenor aided the Elves under Gil-galad yet remaining in Middle-earth. But as time went on, Men rebelled against the Valar and the Elves, over the course of 1500 years, desiring immortality. Tar-Palantir, the penultimate King, repented of the evil of his fathers, but it was too late.