Walter Mazorchuk: Introduction to the category O

The aim of this series of lectures is to give a concise introduction into the algebraic aspects of the Bernstein-Gelfand-Gelfand category O associated with a triangular decomposition of a semi-simple complex Lie algebra. The main focus will be on its highest weight structure, Koszulity and its role in higher representation theory which manifests via a number of interesting functorial actions on this category and its derived category.
A more detailed series of 32 lectures on category O can be found on the Uppsala Algebra YouTube channel.