These lecture notes are based on the first section of Pillay's book  and they cover fundamental notions of stability theory such as definable types, forking calculus and canonical bases, as well as stable groups and homogeneous spaces. The approach followed here is originally due to Hrushovski and Pillay , who presented stability from a local point of view.
Throughout the notes, some general knowledge of model theory is assumed. I recommend the book of Tent and Ziegler  as an introduction to model theory. Furthermore, the texts of Casanovas  and Wagner  may also be useful to the reader to obtain a different approach to stability theory.