  These notes are for the author's lectures, "Integral Reduction and Applied
Algebraic Geometry Techniques" in the School and Workshop on Amplitudes in
Beijing 2016. I introduce the applications of algebraic geometry methods on
multi-loop scattering amplitudes, for instance, integrand reduction, residue
computation in unitarity analysis and Integration-by-parts reduction.
Illustrative examples and exercises are included in these notes.
