Short answers, pulled from the story.
Saxo Grammaticus dedicated the work to Archbishop Anders Sunesen in the year 1208. This dedication marked the completion of a massive literary project commissioned by Absalon, the powerful Archbishop of Lund.
Book fourteen describes the temple located on the island of Rügen during the Northern Crusades and details Danish conquests along the south shore of the Baltic Sea against Slavic peoples. It provides unique information about West Slavic tribes including Polabian Slavs and Pomeranians while covering their pagan beliefs and practices.
Jodocus Badius printed the first complete edition on the 15th of March 1514 in Paris under the title Danorum Regum heroumque Historiae. This Latin version became the source for all existing translations and new editions across Europe.
Christiern Pedersen searched Denmark from 1510 to 1512 to find a surviving copy of the text and finally located a copy in the collection of Archbishop Birger Gunnersen of Lund. He borrowed it and worked with printer Jodocus Badius to prepare the text for publication after most knowledge had come from a summary called Compendium Saxonis found in Chronica Jutensis around 1342.
Books three and four contain the narrative that closely mirrors the famous tragedy performed centuries later. Saxo's story of Amleth served as the primary basis for William Shakespeare's play Hamlet, though in Saxo's version Amleth lives to become King of Jutland unlike Shakespeare's tragic ending.