The topics of this conference organised to honour the 70th birthday of professor Wiesław Pawłucki will evolve around current problems in real analytic and algebraic geometry. In particular, they include such areas as semi-algebraic, semi-analytic, subanalytic, and o-minimal geometry. A special focus will be put on the connections between o-minimality and questions concerning extensions of functions (such as Whitney-type extensions), in the broad sense. As a matter of fact, the peculiarity of the conference theme is that the questions presented and discussed belong to many areas of mathematics: analysis, approximation theory, and singularity theory.