Lecture Note on Curves and Surfaces, 2005, Chuu-Lian Terng

Part 1 is the basics of beginning differential geometry. You just need good multi-variable calculus and linear algebra as prerequisite. (and a little ordinary differential equations)

Part 2 covers pseudospherical surfaces, constant mean curvature surfaces, and minimal surfaces.

Part 1

differential_geometry_2005_1_Chuu-Lian_Terng_28384.pdf

Part 2

differential_geometry_2005_2_Chuu-Lian_Terng_97841.pdf