A sampling of topics including:
1. Positive metric-measure entropy in almost integrable KAM systems, with entropy non-expansion as a bonus;
2. A survival guide for feeble fish in changing fast waters and homogenization of the G-equation;
3. A non-standard approach to spectral properties of the Laplacian in mm-spaces and on connections;
4. Discrete approximations (with an estimate on additive error of distance) for unbounded spaces with bounded geometry.