ASKING THE IMPORTANT QUESTIONS: Who wrote the Torah? For thousands of years people believed that the five books of the Pentateuch were written by Moses. But it couldn't have been, academics say. (Elon Gilad). As usual with Haaretz, read this quickly before it goes behind the paywall.
The answer in this article describes the classical Documentary Hypothesis pretty well, although (1) the second creation story in Genesis uses the divine name YHWH Elohim, not just YHWH, and (2) the idea that the name of the writer of Deuteronomy was Shaphan (cf. 2 Kings 22:8-14) assumes that Deuteronomy was composed during Josiah's reign, whereas many specialists think that what was found in the Temple was an older document (old even in Josiah's time) which eventually served as the basis for our current book of Deuteronomy. In any case, specialists in Pentateuchal source criticism now tend to have some significant reservations about much of the classical Documentary Hypothesis. I have said more on the current state of this question here.
But, yes, everyone agrees that the Pentateuch was written long after the time of Moses, if there was a Moses.