Short answers, pulled from the story.
The History of Middle-earth is a 12-volume series published between 1983 and 1996, collecting and analysing J. R. R. Tolkien's legendarium. It was compiled and edited by his son Christopher Tolkien and documents the evolution of Tolkien's mythological writings from their earliest drafts to his final years.
Christopher Tolkien edited all 12 volumes over a period of roughly 13 years of publication, but spent 45 years in total working on his father's manuscripts. He resigned from his position at New College, Oxford in September 1975 to work exclusively on the editing and moved to the south of France to continue the task.
The series runs to 12 volumes. The first two cover Tolkien's writings from 1914 to 1920; volumes three through five span 1920 to 1937; volumes six through nine document the writing of The Lord of the Rings from 1938 to 1948; volumes ten and eleven cover the later Silmarillion work; and the twelfth volume covers writings from 1960 until Tolkien's death in 1973.
Christopher Tolkien excluded Hobbit material because The Hobbit had not been intended as part of the mythology, was a children's story, and had not originally been set in Middle-earth. Its editorial history was published separately in 2007, edited by John D. Rateliff, in two volumes.
Reviewers described the series as a testament to both Tolkien's creative vision and Christopher's editorial devotion. Wayne G. Hammond and Christina Scull called Tolkien's mythology as documented in the History a work of extraordinary power and scope, and predicted it would start a new era in Tolkien studies. Charles Noad wrote in Mallorn that thorough study of the 12 volumes would be essential for understanding Tolkien's imaginative art.
Scholar Gergely Nagy argued that by editing the manuscripts as a philologist, Christopher inadvertently placed himself in the functional role of Bilbo as editor and collator, reinforcing the effect J. R. R. Tolkien had always wanted: a mythology that appeared to have passed through many hands over a long period. Tolkien had modelled this approach on Elias Lönnrot, the compiler of the Finnish epic the Kalevala.