When I say "theories of the firm", I'm referring, in particular, to the theories exposed in the next works: 1) Transaction Cost Economics exposed in "Transaction Cost Economics" by Tadelis and Williamson (2013) (chapter 4 of "The Handbook of Organizational Economics" by Gibbons and Roberts); 2) Property Rights Theories exposed in "The Costs and Benefits of Ownership" by Grossman and Hart (1986), "Property Rights and The Nature of The Firm" by Hart and Moore (1990), and "Firms, Contracts, and Financial Structure" by Hart (1995); and 3) Incentive System Theories exposed in "The Firm as an Incentive System" by Holmstrom and Milgrom (1994), and "Multitask Principal-Agent Analyses: Incentive Contracts, Asset Ownership, and Job Design" by Holmström and Milgrom (1991).
When I say "Which mathematics", I would appreciate if a list of chapters of a highly recommended math book is given, due to I need to be prepared for analyzing those theories as soon as possible. In this regard, it should be noted that I have studied the first eight chapters of the first volume of Apostol's Calculus. In advance, thanks so much.