Normal Bundle Theorem

Theorem
Let $\tilde M$ be an $m$-dimensional Riemannian manifold.

Let $M \subseteq \tilde M$ be an immersed or embedded $n$-dimensional submanifold with or without boundary.

Let $\valueat {T \tilde M} M$ be the ambient tangent bundle.

Let $NM$ be the normal bundle of $M$.

Then $NM$ is a rank-$\paren {m - n}$ smooth vector subbundle of $\valueat {T \tilde M} M$.