The spatial universe is inherently 3-dimensional, in the sense that wherever we go in the universe, the set of points within a fixed short distance of us forms a 3-dimensional ball. We call a space that has this property a 3-manifold. Mathematicians have spent the last 100 years trying to understand the properties and possibilities for 3-manifolds. This course will be an introduction to 3-manifolds and their applications, including topological, geometric and algebraic aspects. Format: lecture. Evaluation will be based primarily on problem sets and exams. Prerequisites: Mathematics 312 or 315, and Mathematics 301 or Mathematics 323 or Mathematics 324 or both of Mathematics 305 and 321, or Mathematics 305 and permission of instructor. No enrollment limit (expected: 10). This is a quantitative/formal reasoning course.