Lecture 1 - Level curves and locus, definition of parametric curves, tangent, arc length, arc length parametrisation

Lecture 2 - How much a curve is curved, signed unit normal and signed curvature, rigid motions, constant curvature

Lecture 3 - Curves in R^3, principal normal and binormal, torsion

Lecture 4 - Frenet-Serret formula

Lecture 5 - Simple closed curve and isoperimetric inequality

Lecture 6 - Surfaces and parametric surfaces, examples, regular surface and non-example of regular surface, transition maps.

Lecture 7 - Transition maps of smooth surfaces, smooth function between surfaces, diffeomorphism

Lecture 8 - Reparameterization

Lecture 9 - Tangent, Normal

Lecture 10 - Orientable surfaces

Lecture 11 - Examples of Surfaces

Lecture 12 - First Fundamental Form

Lecture 13 - Conformal Mapping

Lecture 14 - Curvature of Surfaces

Lecture 15 - Euler's Theorem

Lecture 16 - Regular Surfaces locally as Quadratic Surfaces

Lecture 17 - Geodesics

Lecture 18 - Existence of Geodesics, Geodesics on Surfaces of revolution

Lecture 19 - Geodesics on surfaces of revolution; Clairaut's Theorem

Lecture 20 - Pseudosphere

Lecture 21 - Classification of Quadratic Surface

Lecture 22 - Surface Area and Equiareal Map