In his introduction to Sefer Devarim, Abarbanel poses a very simple question about this sefer: who wrote it?
Was Sefer Devarim, like the rest of the Chumash, dictated word-for-word from the Almighty to Moshe, or, did Moshe himself compose this sefer with ru'ach ha-kodesh (divine spirit, prophetic powers), much like the later prophets did (Yeshayahu, Yirmiyahu, etc.)? Since the bulk of Sefer Devarim is simply a transcript of Moshe's addresses to Benei Yisrael, one might argue that this sefer is his own creation, just as the prophets would record their prophecies.
Abarbanel cites conflicting pieces of evidence in this regard; several factors appear to indicate that we cannot distinguish this sefer in any way from its four predecessors, whereas others indeed lead us to conclude that Moshe himself composed Sefer Devarim. Let us begin with the indications that this sefer, too, was dictated to Moshe. First and foremost, it is hard to imagine that the Torah, which records for us the direct word of God, would find it appropriate to interject the words of a human being – if even that human being is none other than Moshe Rabbenu. Additionally, Sefer Devarim introduces for the first time several mitzvot which do not appear anywhere earlier in the Torah (for example, the mitzva of yibum – 25:5-10). If Moshe himself wrote this sefer, how could he add mitzvot; is this not the exclusive realm of the Almighty? Finally, and perhaps most conclusively, Chazal explicitly comment (Sanhedrin 99a) that whoever claims that even a single verse in the Torah was written by Moshe, rather than by the Almighty Himself, is considered a heretic. Seemingly, then, we can draw no distinction between Sefer Devarim and the first four Chumashim, and they were all dictated directly from God to Moshe.
On the other hand, Abarbanel notes, one can raise convincing arguments in the opposite direction, as well. For one thing, although, as mentioned, Sefer Devarim does seem to introduce new mitzvot, it also rehashes many mitzvot discussed previously in Chumash. This repetition is easily understood if we view this sefer as Moshe's own composition. He perhaps felt that certain laws required further clarification or emphasis and therefore chose to repeat it. If, however, God Himself wrote this sefer, then why did He not provide sufficient clarification or emphasis the first time? Secondly, the overwhelming majority of Sefer Devarim is written in first person, from the perspective of Moshe himself, implying that it is he, rather than God, speaking. Finally, Chazal themselves, towards the end of Masekhet Megila, draw a distinction between Devarim and the earlier sefarim in this regard. The Gemara says that the tokhecha section (describing the blessings and curses that will befall Benei Yisrael for their compliance with or neglect of the Torah) in Sefer Vayikra was said by God, whereas the tokhecha in Devarim was told by Moshe himself.
How can we reconcile all these conflicting pieces of evidence?
Abarbanel suggests a very simple explanation. Seeing that his end was drawing near, Moshe Rabbenu assembled Benei Yisrael for a final series of addresses containing words of admonition and a review of mitzvot that he found it necessary to clarify or emphasize. Afterward, God told Moshe to include this series of lectures in the Chumash as part of the Torah. He then dictated to Moshe word-for-word Sefer Devarim, with perhaps certain changes from the original presentations, such that Sefer Devarim became part of Chumash on a level equal to that of the first four sefarim.
This resolves all the issues raised earlier except for one. What about the mitzvot introduced for the first time in Sefer Devarim? If this sefer was originally narrated by Moshe, how could he come up with his own mitzvot? Abarbanel therefore contends that in truth, Sefer Devarim does not contain any new mitzvot not found earlier in the Torah. If one searches hard enough, he claims, he can trace the origin of every "new" mitzva in this sefer somewhere earlier in Chumash. (Yibum, for example, can be said as having originally appeared in Parashat Vayeishev, in the story of Yehuda and Tamar.) Indeed, throughout his commentary to Sefer Devarim, Abarbanel makes a point of informing his readers of where all seemingly new mitzvot in Sefer Devarim initially appeared earlier in the Chumash.