Lecture Notes on O Minimal Structures and Real Analytic Geometry This volume was produced in conjunction with the Thematic Program in o Minimal Structures and Real Analytic Geometry held from January to June of 2009 at the Fields Institute. Five of the six contributions consist of notes from graduate courses associated with the program: Felipe Cano on a new proof of resolution of singularities for planar analytic vector fields; Chris Miller on o minimality and Hardy fields; Jean Philippe Rolin on the construction of o minimal structures from quasianalytic classes; Fernando Sanz on non oscillatory trajectories of vector fields; and Patrick Speissegger on pfaffian sets. The sixth contribution by Antongiulio Fornasiero and Tamara Servi is an adaptation to the nonstandard setting of A.J. Wilkies construction of o minimal structures from infinitely differentiable functions. Most of this material is either unavailable elsewhere or spread across many different sources such as research papers conference proceedings and PhD theses. This book will be a useful tool for graduate students or researchers from related fields who want to learn about expansions of o minimal structures by solutions or images thereof of definable systems of differential equations. Preface Blowings up of Vector Fields (F. Cano) Basics of o Minimality and Hardy Fields (C. Miller) Construction of o Minimal Structures from Quasianalytic Classes (J. P. Rolin) Course on Non Oscillatory Trajectories F.S. Sánchez) Pfaffian Sets and o Minimality (P. Speissegger) Theorems of the Complement (A. Fornasiero T. Servi).