The critical problems of the Third Decade of Livy have long been familiar to students. In Books XXI.–XXV. we have only the mutilated Codex Puteanus (P) of the fifth century and later manuscripts derived from it, directly or indirectly, at one or more points in its history. R, C, and most probably M, are copies of P, after it was corrected by P2 and probably P3. Here the problem in the parts in which P is preserved is to correct its numerous corruptions by conjecture as far as possible; and, where it is now defective, by comparing the later MSS. to arrive at their inter-relation and at P's original text, and then subject this text to the same process of criticism. Also a study of the corrections in the earlier of these MSS. may reveal the previous existence of other traditions and of other MSS. now lost—such corrections, e.g., as are made by P4, R2, and M2.