The Mobius strip; collapsing the equator; exploding a point in the plane; geometric definition of blowups; the secant construction; pull-backs of curves under blowup.

The algebraic definition of blowups; the blowup in affine charts; birational maps; the strict and total transforms of varieties and vector fields.

Axiomatic definition of blowups; Cartier divisors; base change property; persistence properties.

First examples of resolutions; curves and surfaces; effect of blowups on polynomials; singularity invariants; lexicographic orderings.

Choice of centers of blowup; descent in dimension; lexicographic decrease of invariant; transversality; obstructions in positive characteristic; resolution of planar vector fields.