Explore complex analysis in o-minimal expansions of real closed fields in this comprehensive lecture by Kobi Peterzil from the University of Haifa. Delve into topics such as removal of singularities, differentiable functions, elementary extensions, and all-minimality. Examine key theorems and power series applications within the context of o-minimality. Part of the Graduate Course on O-minimality and Applications at the Fields Institute, this in-depth presentation offers valuable insights for advanced mathematics students and researchers.