Short answers, pulled from the story.
The Silmarillion was published posthumously by J. R. R. Tolkien's son, Christopher Tolkien, in 1977. Christopher was assisted in editing the manuscript by the Canadian writer Guy Gavriel Kay, who spent a year working on the project with him in Oxford. The first edition was brought out in hardback by Allen & Unwin.
The Silmarillion has five sections: Ainulindalë, a creation narrative; Valaquenta, describing the Valar and Maiar; Quenta Silmarillion, 24 chapters covering the history of the First Age and the wars over the Silmarils; Akallabêth, recounting the fall of Númenor in the Second Age; and Of the Rings of Power and the Third Age, which summarises the events leading to The Lord of the Rings.
Tolkien worked on The Silmarillion from 1914 until his death, but the project remained unfinished for several reasons. His publisher rejected an early version in 1937, calling it obscure and "too Celtic", and asked him to write a sequel to The Hobbit instead. In the late 1950s he became absorbed in theological and philosophical questions about the mythology rather than its narrative, and he developed doubts about fundamental aspects that stretched back to the earliest versions of the stories.
The Silmarillion drew on the Finnish epic Kalevala, particularly the tale of Kullervo. Greek mythology shaped both the island of Númenor, which parallels Atlantis, and the Valar, who resemble the Olympian gods. Norse mythology influenced the Valar as well, with parallels to the Æsir of Asgard. Medieval Christian cosmology, especially St. Augustine's writings on music and the concept of divine harmony, shaped the Ainulindalë creation narrative. Celtic mythology, including Irish legends of the Tuatha Dé Danann, influenced the exile of the Noldorin Elves.
The Silmarillion was commercially successful, topping The New York Times Fiction Best Seller list in October 1977 and winning the Locus Award for Best Fantasy Novel in 1978. Critical reception was largely negative; Tolkien's publisher described the reviews as "among the most unfair he had ever seen". The book has sold over a million copies and has been translated into at least 40 languages, though those figures are far below The Hobbit and The Lord of the Rings, which have each sold over 100 million copies.
Scholars note that the 1977 book was not authorised by J. R. R. Tolkien, who did not write all of it and did not define the frame in which it was to be presented. Christopher Tolkien had to invent story elements to fill narrative gaps, most notably in the chapter "Of the Ruin of Doriath", which had been untouched since the early 1930s. Randel Helms stated in 1981 that the published Silmarillion "is the invention of the son not the father". Douglas Charles Kane's 2009 book Arda Reconstructed documents exactly which sources and editorial decisions Christopher used to construct the text.