As John Sailhamer says (The Meaning of the Pentateuch, page 70), most OT books are anonymous and we have no way of knowing who wrote them. This applies as much to the Pentateuch as to any other book of the Bible, except those with specific authorship notations. On page 23, Sailhamer asks whether Moses was really the author of the Pentateuch. He does not find the answer to this question within the texts, but in Joshua 1:8 and John 5:46:
Joshua 1:8: This book of the law shall not depart out of thy mouth; but thou shalt meditate therein day and night, that thou mayest observe to do according to all that is written therein: for then thou shalt make thy way prosperous, and then thou shalt have good success.
John 5:46: For had ye believed Moses, ye would have believed me: for he wrote of me.
Sailhamer seeks to resolve the issues that speak against a single author, by assuming that a later editor took over and, for some reason, rewrote what Moses had already written. According to Sailhamer (page 24), the last edition of the Pentateuch was written late, after the time of Malachi. He calls this an evangelical view, but it is far from the most well supported explanation.
Does anyone know of other viable theories
The most common theory is known as the Documentary Hypothesis. The Documentary Hypothesis defines four independent sources (JEDP) for the Pentateuch, which not only explains the changes in authorship style, theology and early to late Hebrew language, but also the frequent use of the third person in regard to Moses.
The Documentary Hypothesis, as originally proposed by Wellhausen, is no longer accepted by the majority of biblical scholars as definitive but, with various proposed modifications under consideration, it remains the best explanation we have for the development of the Pentateuch. Joel S. Baden says, in 'The Re-Emergence of Source Criticism: The Neo-Documentary Hypothesis' that European scholarship abandoned the JEDP hypothesis during the second half of the twentieth century, as American scholars continued to support it. He says this situation is changing, as the Documentary Hypothesis is regaining its place as a viable, productive, and current approach to the Pentateuch. One of the main contributions of more recent source-critical work has been the identification and correction of the methodological problems that plagued earlier scholarship and had contributed to the move away from the Documentary Hypothesis in Europe in recent generations. The Documentary Hypothesis has been worked over, revised, criticised and redefined by numerous scholars for well over a century and has survived as a viable theory.