\(\def\Real{\mathbb{R}}

\def\Comp{\mathbb{C}}

\def\Rat{\mathbb{Q}}

\def\Field{\mathbb{F}}

\def\Fun{\mathbf{Fun}}

\def\e{\mathbf{e}}

\def\f{\mathbf{f}}

\def\torus{\mathbb{T}}

\)

*Manifolds* are topological spaces that locally look like Euclidean spaces.

Formalism: charts and atlases. Beware of pathologies (long line; double point…)! Smooth manifolds vs. topological ones.

*Inverse function theorem* (for a …