The distinctive approach of Henderson and Taimina's text stimulates students to develop a broader, deeper understanding of mathematics through active experience—including discovery, discussion, writing fundamental ideas and learning about the history of those ideas. A series of interesting problems (ranging from easy to challenging) encourage students to gather and discuss their reasonings and understanding. This is the only undergraduate text that pays attention to geometric intuition, student cognitive development, and rigorous mathematics; and that includes a broad vision of geometry that leads to discussion of four strands in the history of geometry and to an understanding of the possible shapes of the physical universe.