“the Book of the Law.” This was actually a scroll. One scroll could not hold the entire Torah, so this is either a scroll with part of the Torah on it, or a collection of scrolls with all the Torah on it.
“the Law of Yahweh given by the hand of Moses.” The Hebrew is “the torah of Yahweh,” where “torah” is much more than “law.” The torah involves instruction in many different ways (see commentary on Prov. 1:8). The phrase “given by the hand of Moses” almost certainly means that this was a copy of what had been written by Moses. However, it is possible that Moses actually wrote some of what they found.