Braided Geometry and its applications

By Braided Geometry I mean that related to a braiding, i.e. a special type solution of the Quantum Yang–Baxter Equation. In the frameworks of this geometry certain notions of classical or super-geometry (traces, Lie algebras, vector fields, orbits in $g^*$) are replaced by their braided counterparts. In my talk I plan to deliver a shot review of basic notions and recent results.