• Denjoy-Carleman class
• o-minimality
• quasi-analytic
• resolution of singularities
• Weierstrass division
• Weierstrass preparation

The thesis is a compilatory work on quasi-analytic Denjoy-Carleman functions, meaning classes of real functions defined by bounds on the successive derivatives which contain no flat function.
After an introduction to the matter, we include result concerning the algebraic properties of the local rings of germs of quasi-analytic functions and with the geometric properties of quasi-analytic manifolds and sets.
Particular importance is given to the failure of the Weierstrass division and preparation theorems in quasi-analytic classes and the related open problem of noetherianity of the local rings is touched upon.
On the side of quasi-analytic sets, we report results on resolution of singularities, which can sometimes suffice in lieu of the preparation theorem. We also show how to derive model theoretic properties of quasi-analytic functions from resolution of singularities and why said results are relevant in model theory.
We close by relaying some of the more recent developments in the field of quasi-analytic classes.