Interior, closure, and boundary: pdf. Product topology: pdf. Topologists' sine curve: pdf. Hyperplane complements: pdf. Gram-Schmidt and connectedness: pdf. Compactness review: pdf. Compactness criteria: pdf. Completion of metric spaces: pdf. Quotient vector spaces: pdf. Real quadratic spaces: pdf. Geometric approach to signature pdf. Gluing topologies: pdf. Construction of tensor products: pdf. Calculations and further examples with tensor products: pdf. Maps with tensor products: pdf. Higher derivatives and multilinear Taylor's formula: pdf. Bases of symmetric and exterior powers: pdf. Tensor algebra and tensor pairings: pdf. Topology of projective space: pdf. Calculations with symmetric and exterior powers: pdf. Paracompactness and local compactness: pdf. Products of manifolds: pdf. Atlases and differentiable structures: pdf. Morse Lemma: pdf. Manifolds with corners: pdf. Quotients by group actions: pdf. Orientations: pdf. Global/local and bump functions: pdf. Derivative mappings, parametric curves, and velocity vectors: pdf. Tangent spaces and products: pdf. Mobius strip in 3-space: pdf. Local structure theorem: pdf. Bijectivity and isomorphism: pdf. Hodge star: pdf. Submersions and transversality: pdf. Construction of vector fields pdf. Derivations and vector fields: pdf. Modules and derivations: pdf. Maps of bundles and O-modules: pdf. Linear ODE: pdf. Direct sum of bundles: pdf. Equivalence of bundles and O-modules: pdf. Integral curves: pdf. Pullback and transition matrices: pdf. Bundle operations: pdf. Subbundles and quotient bundles: pdf. Universal and normal bundles: pdf. From integral curves to integral manifolds: pdf. Example of integral manifold: pdf. Determinant bundles: pdf. Frobenius theorem and vector fields: pdf. Operations with metrics: pdf. Graph metric tensor: pdf. Universe is not a 4-sphere: pdf. Orientation on bundles and manifolds: pdf. Coordinate-free d-map on forms: pdf. The map-maker's paradox pdf. Gauss map and scalar curvature: pdf. How to compute integrals: pdf. Stokes' theorem on Riemannian manifolds: pdf. Maxwell's equations: pdf. Stokes' theorem with corners: pdf. Smooth hairy ball theorem pdf. Covariant derivatives and parallel transport: pdf.