Leonid Makar-Limanov: A new proof of the cancellation theorem Abstract: We present a complete and elementary proof using AK-invariant that if $S \times K^1 \simeq K^3$, where $K$ is an algebraically closed field of any characteristic and $S$ is a surface then $S \simeq K^2$ with added explanation, unfortunately not as elementary, that factorial surfaces cannot be used to produce the Danielewski type counterexamples.