Partial isometires of intervals: dynamics, geometry and topology

Systems of partial isometries of the interval represent a simple combinatorial object which appears in topology in connection with measured foliations on a surface (orientable or non-orinetable), in dynamics as a nice model to study billiards in rational polygons and in geometric group theory as a way to describe actions of free groups on R-trees.
We will discuss several classes of systems of isometries including interval exchange transformations, interval exchange transformations with flips, observe briefly matin motivational problems to study them and compare their basic dynamical properties: minimality, ergodicity, invariant measures etc.