I teach Bible and so the main text is the biblical text. These are three biblical books I love to teach to undergraduates:

Ecclesiastes

An intellectual engagement about a perennial problem: the meaning of life. Non-religious students can feel as at home as religious students, if not more so.

Isaiah 40–66 (Second Isaiah)

Amazingly strong language and imagery. Students get to see that a prophetic message has rhetorical force; it is not just pious or pretty words.

Proverbs

I actually don't like Proverbs that much but the students always like it. They relate to it like a "how-to" book. And its parts are short enough to text or Twitter. They find the sayings relevant to their own lives, especially once they understand that the book is advice to adolescent males. They are surprised to learn that this is "establishment" literature, designed to make the next generation conform to society.