The Greek word Pentateuch (five books or a bookcase or volume of five) refers to the first five books of the Bible; Genesis, Exodus, Leviticus, Numbers, and Deuteronomy. To the Jews, these five books are also known collectively as The Torah. For thousands of years, the prophet Moses was regarded as the sole author of the first five books of the Bible.
The Torah breaks down in the following books:

Genesis Creation of the world, the Fall of man into sin, the Flood that covered the earth, and the Patriarchs Abraham, Isaac, and Jacob. Within these first 50 chapters of the Bible, we get to explore the origins of the world. We see God pouring his heart into the creation of the world, only for the world to turn on its heels in Genesis 3 and plunge into sin. We meet the patriarchs of Israel (the Founding Fathers) and get to learn about their lives and stories. We end with the son of the patriarch Jacob, named Joseph, who takes up the narrative from Genesis 37-50.

Exodus The escape of the Israelites from their slavery in Egypt, and Moses receiving the Ten Commandments. After Joseph has his family settle in Egypt, the Israelites numbers grow. The Egyptians, fearful of other enemies as well as the Israelites, force the Israelites into 400 years of brutal slavery. God eventually sends Moses to free the people of Israel. They escape Egypt, and God gives Moses a list of commandments by which the Israelites must follow.

Leviticus Laws, festivals, and observances of the Jewish people. Piggybacking off of Exodus, while the Israelites wander the desert, they begin to recover as a nation. God lays down laws and statutes they must observe for rightful living with one another. He also institutes many holidays and observances, still practiced to this day. We learn about each of these holidays in this book. 

Numbers The years the Israelites spent wandering in the desert. Don't let the average Joe fool you, this isn't a boring book. It's full of war stories, spies, and talking donkeys. While the Israelites were heading into a land of their own, after their slavery in Egypt, they spent several decades wandering the desert, partially because of their stubbornness and disobedience to God. In Numbers, we receive the desert narratives. We see God providing for them in the wilderness. 

Deuteronomy More laws for the Jewish people. Piggybacking off of Leviticus, we see more laws for the Jewish people. These show us how far each human has fallen from grace and how much we need Jesus to come to our rescue. The narrative concludes with Moses' passing and Joshua taking the reins and leading the Israelites into the land they were promised.