Reference request:classical theory of curves and surfaces in the language of manifolds.

Question

For some reason,I learnt some theory of manifold before I learn classical theory of curves and surfaces (I have read Loring Tu's 'An introduction to manifolds.')Then I want to learn Riemann geometry but I know that Riemann geometry requires classical theory of curves and surfaces.But books on classical theory now seem uncomfortable to me.Maybe I need some book using modern language to inroduce these classical theory.Any help will be thanked.