We shall take these three groups in order. The Multituberculata have already been to some extent defined, if such a word can be used to express the summation of the very scanty information at our disposal. Of this group, _Plagiaulax_ is a genus which occurs in the Purbeck beds; it is only known by lower jaws implying an animal of the size of a Rat or rather smaller. The jaws have in front a large incisor which looks Rodent-like, and also like those of the Diprotodont Marsupials; but it is held that these teeth did not grow from persistent pulps, and there is in any case no anterior thickened coating of enamel. Canines are absent; the diastema is followed by four premolars increasing progressively in size and possessing somewhat complicated grinding surfaces. These surfaces are formed by several obliquely-set ridges. The succeeding teeth are termed molars on account of their difference in structure, and there are but two of them on each side. The molars are of a pattern common in the Multituberculata; the centre is hollowed, and the raised rim is beset by tubercles. Other Jurassic genera of Multituberculates are _Bolodon_, _Allodon_, and _Stereognathus_. All of these possess the same multituberculate molars. Of the Triconodonta the type-genus is _Triconodon_. This genus is better known than most Jurassic mammals, since both the upper and the lower dentition have been described. It appears to have possessed the typical Eutherian dentition of forty-four teeth, to which a fourth molar is added in some species. The great difference between the molars and premolars argues a complete tooth-change. The genus is American as well as European. _Spalacotherium_ has more molars, five or six. _Phascolotherium bucklandi_, on the other hand, is a much older type in the form of its teeth. There are, however, not so many of them as in _Amphitherium_; _Phascolotherium_ has but two premolars and five molars, making a total of forty-eight teeth. The teeth are of the triconodont form, the three cusps being in line, and the middle one the largest. {100} _Amphilestes_ has teeth of the same pattern but has more of them, the premolars and molars being respectively four and five. All these animals had the lower jaw inflected. Whether they are all Marsupials or not, it is clear that _Phascolotherium_ and _Amphilestes_ should be united and placed away from _Amphitherium_ on account of the more primitive form of their teeth. We next come to the Trituberculata.