Moses is credited by tradition with the Torah, the first five books of the Hebrew Bible, and the attribution is one of the oldest and most thoroughly examined problems in biblical scholarship.
The internal difficulties are visible without any theory. Deuteronomy narrates Moses' death and burial and adds that no one knows his grave to this day, which is an odd thing for him to write. The books contain two creation accounts with different sequences and different names for God, two interleaved flood narratives with different numbers of animals and different durations, and repeated doublets where the same event happens twice in different words. Laws contradict one another on where sacrifice may be offered and on the treatment of slaves.
The classical analysis, given its influential form by Julius Wellhausen in 1878, distributed the material among four sources, conventionally J, E, D and P, composed at different periods and combined by editors, with the priestly material late and the whole assembled after the exile. The four-source model has since been heavily criticised and substantially revised; there is no current consensus replacing it, and European and North American scholarship have diverged. What is not in dispute among critical scholars is that the Torah is composite, that it reached its form long after the period it describes, and that Mosaic authorship is a traditional ascription rather than a historical claim.
Traditional Judaism, and some conservative Christian scholarship, hold to Mosaic authorship or to a substantial Mosaic core. That position exists and should be named rather than ignored.