This talk is devoted to generalization of subanalytic geometry to quasianalytic classes. A starting point are quasianalytic functions- smooth functions which share some important properties with analytic functions like analytic continuation, however their Taylor power series are not necessarily convergent.

During this talk the definition and basic properties of quasianalytic functions will be provided. This will be the starting point to the geometry in quasianalytic classes. The similarities and differences of geometry in quasianalytic classes and subanalytic geometry will be discussed. We will also present the theorem which states some equivalences between certain properties of closed sub-quasianalytic sets like composite function property, semicontinuity of diagram exponents or uniform Chevalley estimate.