Is there any good reference that makes the theory of manifolds in $\mathbb{R}^N$. Especially area, coarea formulae, curvatures for submanifolds of $\mathbb{R}^N$, Differentiability, Vector fields, Lie brackets, Operators, Surface theory, operators, tensor, forms, bundles...and all the staff.
It is above my level to understand manifold theory in abstract context from a place on...