The only surviving source for the Havamal is the Codex Regius (Latin for "The King’s Book"), an Icelandic manuscript from the 13th Century. The Codex Regius was lost until 1643 when it came into the possession of a bishop in Iceland who sent it to King Frederick III of Denmark as a gift. It was at this time that the manuscript came to be known as “The King’s Book”.
The Codex Regius is an important book for the Norse as it carries many of the myths and legends from their history. Scholars believe that the first section of the Havamal is the oldest portion of the Havamal. How old? Unfortunately, we may never know. Much of the Norse myths and legends were not written down by the Norse. Though they did have a written language of sorts in the form of the runes, they did not write down much. The runes were typically used in charms, writing one's name, and some memorial stones in which one wrote down a significant event or in memory of an ancestor.
The Codex Regius was written and translated by Christianized Norse, probably monks, who wished to preserve the stories of their ancestors. As I read the Havamal, I got the impression that they were just writing down the old sayings and stories that they remember their grandparents told them as they noticed that these sayings and stories were becoming lost in the new Christian Scandinavia. I find it doubtful that they wrote down all of the stories that told by the ancient Norse, but I am hopeful that someday we will discover yet a new book with even more stories and poems.