Industrial organization is the field of economics that studies the behavior of firms and the structure of markets when markets fail to be perfectly competitive. Theoretical analysis in the field is heavily based on game theory.
The common market structures studied in this field are the following:
A standard graduate textbook in the field is "The Theory of Industrial Organization" by Jean Tirole (The MIT Press, 1988). This book requires extensive knowledge of calculus as well as game theory.
Anyone new to the field of economics should begin with a standard undergraduate text "Industrial Organization: Theory and Application" by Oz Shy (The MIT Press, 1995).