But we have seen that Absalon died in 1201, and that Bk.

xi, at any rate, was not written after 1202.

It almost certainly follows that the latter books were written in Absalon's life; but the Preface, written after them, refers to events in 1208.
Therefore, unless we suppose that the issue was for some reason delayed, or that Saxo spent seven years in polishing--which is not impossible--there is some reason to surmise that he began with that portion of his work which was nearest to his own time, and added the previous (especially the first nine, or mythical) books, as a completion, and possibly as an afterthought.

But this is a point which there is no real means of settling.

We do not know how late the Preface was written, except that it must have been some time between 1208 and 1223, when Anders Suneson ceased to be Archbishop; nor do we know when Saxo died.
HISTORY OF THE WORK.
Nothing is stranger than that a work of such force and genius, unique in Danish letters, should have been forgotten for three hundred years, and have survived only in an epitome and in exceedingly few manuscripts.