We know Saxo Grammaticus almost exclusively through the text of Gesta Danorum, an ample and stylistically ambitious prosimetrum tracing the history of Denmark from prehistory down to Saxo's time. Through references in the text to Danish royal and ecclesiastical matters, and from a few brief mentions or probable mentions of him elsewhere, it seems certain that he was at work on the project during the decades just before and just after 1200 and likely that he was a secular cleric within the archbishopric in Lund. Denmark was the dominant power in the North, and Saxo celebrated it in a work of sixteen books divided into groups of four, the first three of which end with a major event: the first with the birth of Christ; the second with the coming of Christianity; the third with the establishment of the archiepiscopal see in Lund; the last group treats the period 1104-1187. Saxo probably studied abroad, and the greatest influence on his style was Valerius Maximus.
The 1931 critical edition of Jørgen Olrik and Hans Ræder was long known to be imperfect,  and Karsten Friis-Jensen, who up to his untimely death in 2012 continued to contribute insightful scholarship on Saxo scholarship, undertook to edit the text anew. Peter Zeeberg worked in tandem with him to produce a Danish translation, and the publication of their joint effort in 2005 gave the world a new trustworthy standard edition of Saxo and those who could read Danish a facing-page translation (Zeeberg's translation had also been published separately in 2000).  The 2005 edition contained an English translation of the Danish version of Friis-Jensen's introduction offering meticulous treatment of editorial principles, and back matter treating Saxo's meters, a register of textual parallels followed by an index of authors in the register, and an index of personal names. It was welcome indeed.
Outside Denmark, Gesta Danorum had primarily attracted interest for the accounts of pre-Viking and Viking Age matters and translations of vernacular poetry, some of it extant, some lost. The first nine books can easily be put alongside the vast vernacular literature of Iceland and Norway that was beginning an explosive expansion around and just after the time when Saxo was at work. Saxo mentions Icelanders as excellent sources, and he has versions of many of the most compelling narratives in Old Icelandic tradition, mythical and heroic. To cite just a few, the Euhemerized gods Odin, Thor, and the doomed Baldr fight in epic battles and vie for succession. Like many heroes, the prehistoric king Frotho kills a dragon, and Hrolf kraki and his men fall in a famous battle. The Odinic hero Starkatherus betrays kings in a long unhappy life. Much of what we find in some of the most famous works from medieval Iceland, including mythological and heroic poetry, Snorri Sturluson's Edda, and the so-called fornaldarsögur (sagas of antiquity; that is, of the heroes who lived and died before Iceland was settled) find parallels or echoes in Gesta Danorum.
As a result of such parallels and echoes, book 9 was the stopping point in the translations of Oliver Elton (1895) and Peter Fisher (Davidson and Fisher 1979-80).  The latter was equipped with an extensive commentary by Hilda Davidson focusing precisely on the parallels between Saxo's text and Old Norse-Icelandic material (Davidson and Fisher 1979-1980), complementing an earlier commentary to those same first nine books by Paul Hermann (1922).  Furthermore, perusing the bibliography, I found translations of books 1-9 not only into English and German but also into French, Italian, Japanese, and Spanish. And yet in book 10 both Cnut the Great and Olaf the Saint enter the story, and the following books offer a fascinating and invaluable picture of the end of the Viking Age and beginning of the Middle Ages in Denmark, parallel to the Old Norse-Icelandic kings saga compilations Morkinskinna, Fagrskinna, and Heimskringla. Although these later books from the Gesta Danorumwere translated into English by Erik Christiansen (2001), with commentary, there was still no complete English translation. 
In the work under review, the 2005 edition of Friis-Jensen appears with only minor modifications.  A facing-page English translation by Peter Fisher, based on his 1979 translation of the first nine books and with a new translation of the rest, offers a complete English translation. Maps and genealogical tables have been added, and the introduction is augmented to contain discussion of the author and his background, and a presentation of important issues regarding the text: time of composition, title of the work, structure, themes, language and models, poetry and poets, sources, and influences. Much of this content distills earlier scholarship of Friis-Jensen, some of which was written in Danish. This Introduction now comprises the most lucid introduction to Saxo and Gesta Danorum available anywhere. In addition, the discussion of editorial principles is carried forward, somewhat modified from the 2005 edition, and Fisher's Translator's Introduction replaces Zeeberg's. The metrical key is moved from back to front matter and is now in English. Back matter includes the Register of Parallels, and an Index of Quotations and Allusions presents the 2005 Index of Authors in the Register of Parallels in a fashion that is slightly more systematic and a good deal clearer on the page. Fisher was responsible for the new General Index, which includes not only names but also such topics as Madness, Magic, and Marriage, and thus offers an independent tool for entry into Saxo's long and complex text.
This version of Friis-Jensen's excellent edition, with its excellent translation and the tools in the front and back matter, make Saxo accessible to international scholarship and the international reading community in a way that the Danish edition, exemplary as it is, simply could not do. It is an extremely important contribution to the study of the Nordic Middle Ages and the European twelfth-century renaissance.
1. Jørgen Olrik, and Hans Ræder, Saxonis Gesta Danorum (Copenhagen 1931).
2. Peter Zeeberg (trans.), Saxos Danmarkshistorie (Copenhagen: Det danske Sprog- og Litteraturselskab & Gad, 2000).
3. Oliver Elton (trans.), The First Nine Books of the Danish History of Saxo Grammaticus (London 1905); Hilda Ellis Davidson (ed.), and Peter Fisher (trans.), The History of the Danes, Books I-IX (Woodbridge, Suffolk: D. S. Brewer, 1979-1980).
4. Paul Herrmann, Erläuterungnen zu den ersten neun Büchern der dänischen Geschichte Leipsig 1922).
5. Eric Christiansen (trans.), Danorum regum heroumque historiae a Saxone Grammatico conscriptae. Books X-XVI. The Text of the First Edition with Translation and Commentary, 3 vols (BAR International Series, 84; Oxford: B.A.R, 2001).
6. Karsten Friis-Jensen (ed.), and Peter Zeeberg (trans.), Saxo Grammaticus. Gesta Danorum. Danmarkshistorien (Copenhagen: Det danske Sprog- og Litteraturselskab & Gad, 2005).