Graphs and level sets -- Vector fields -- The tangent space -- Surfaces -- Vector fields on surfaces; orientation -- The Gauss map -- Geodesics -- Parallel transport -- The Weingarten map -- Curvature of plane curves -- Arc length and line integrals -- Curvature of surfaces -- Convex surfaces -- Parametrized surfaces -- Local equivalence of surfaces and parametrized surfaces -- Focal points -- Surface area and volume -- Minimal surfaces -- The exponential map -- Surfaces with boundary -- The Gauss-Bonnet theorem -- Rigid motions and congruence -- Isometries -- Riemannian metrics