Volume 1 Lengths-The Pythagorean theorem Consequences of the Pythagorean theorem Areas Areas by slicing and scaling Areas by cut and paste Areas by counting Unsolvable problems in Euclidean geometry Does every set have a size? Bibliography Volume 2 The fundamental theorem of algebra The Brouwer fixed point theorem Tools Lebesgue covering dimension Fat curves and Peano curves The arc, the simple closed curve, and the Cantor set Algebraic topology Characterization of the 2-sphere 2-manifolds Arcs in $\mathbb{S}^2$ are tame R. L. Moore's decomposition theorem The open mapping theorem Triangulation of 2-manifolds Structure and classification of 2-manifolds The torus Orientation and Euler characteristic The Riemann-Hurwitz theorem Bibliography Volume 3 A graphical introduction to hyperbolic geometry Hyperbolic geometry Gravity as curvature Curvature by polyhedral approximation Curvature as a length derivative Theorema egregium Curvature appendix Bibliography.