An Introduction to Surfaces - Differential Geometry

Explore the fundamental concepts of surfaces in differential geometry through this comprehensive lecture. Delve into the key notion of orientability and examine the division between algebraic and parametrized surfaces. Gain insights into important examples of surfaces, including quadrics like spheres, ellipsoids, and hyperboloids, as well as more unusual examples such as the Oloid. Learn about the balanced approach between algebraic and parametric perspectives, with a focus on providing more detail on algebraic surfaces. Discover the main objects of interest in differential geometry and develop a solid foundation for further study in this field.

Introduction
Smooth orientable surfaces
Orientable surfaces
Algebraic and parametric surfaces
Parametric surfaces
Riemann surfaces
Planes
Spheres
Revolutions
No Lloyd