I am looking for an English translation of Voronoi's doctoral dissertation, "On a generalization of the Algorithm of Continued Fractions." I can only find it in the original Russian.
"The Theory of Irrationalities of the Third Degree" is much more clere than original Voronoi's doctoral dissertation. There are some recent works on Voronoi's and Minkowski's algoritms. You can start for example from http://www.springerlink.com/content/g364t1u85r103584/