In these 4 lectures I intend to cover the following subjects.

I. Basics of o-minimality

(1) Monotonicity Theorem

(2) Cell decomposition

(3) Consequences of Cell decomposition.

II. More advanced properties

(1) Triangulation and Euler Characteristic

(2) Piecewise smoothness

III. Hardy Fields, valuations and elementary extensions

(1.) Hardy fields, valuations and elementary extensions

(2.) Growth Dichotomy

(3.) Hausdorff Limits

(4.) Real closed valued fields

(5.) T-convexity

(6.) Bieri-Groves Theorem