## Manifolds

What is manifold?

Manifold is a set, and also a topological space

Smoothness

Smooth structure

Definition of manifold

Equivalence relation on atlases

Smooth maps between manifolds

The notion of o-little

Cotangent space

Tangent space

Tangent bundle

Tangent bundle: transition functions

Consistency condition on the transition functions

Derivatives of maps

Category of smooth manifolds