By Braided Geometry I mean a theory dealing with braidings (i.e. solutions of the Quantum Yang-Baxter Equation) playing the role of the usual flip or (super-flip). One of the main object of Braided Geometry is the so-called Reflection Equation algebra associated to a given braiding. This algebra can be treated as an analog of the enveloping algebra U(gl(m|n)). Besides, for a matrix coming in its definition there is an analog of the Cayley-Hamilton identity. Also a version of partial derivatives can be defined on this algebra. In my talk I plan to describe a way of getting an analog of the Calogero-Moser system by using the mentioned properties of the Reflection Equation algebra.