What are some good books and articles about the principal-agent problem? I'm looking for introductory academic books/articles or "popular-science" kind of ones.
In my PhD program everyone was using The Theory of Incentives: The Principal-Agent Model by Jean-Jacques Laffont and David Martimort. It offers a formal and relatively complete treatment without being too technical. I haven't read any other book on the topic, so unfortunately I cannot compare.
If you want to avoid any mathematical formalism, a good introductory article and literature review on the topic is Incentives in Principal-Agent Relationships by David E.M. Sappington, in the Journal of Economic Perspectives (1991).
Finally, I would also recommend that you have a look at the Nobel lectures by Hart and Holmström on contractual relationships inside organizations.
I found "Contract Theory" by Patrick Bolton and Mathias Dewatripont to be a very nice and thorough book. It, however, might be too advanced, although you can skip the formalism and just read the intuitions provided. Let me quote how the book is advertised:
The book emphasizes applications rather than general theorems while providing self-contained, intuitive treatment of the simple models analyzed. In this way, it can also serve as a reference for researchers interested in building contract-theoretic models in applied contexts.The book covers all the major topics in contract theory taught in most graduate courses. It begins by discussing such basic ideas in incentive and information theory as screening, signaling, and moral hazard. Subsequent sections treat multilateral contracting with private information or hidden actions, covering auction theory, bilateral trade under private information, and the theory of the internal organization of firms; long-term contracts with private information or hidden actions; and incomplete contracts, the theory of ownership and control, and contracting with externalities. Each chapter ends with a guide to the relevant literature.
"The Economics of Contracts" by Bernard Salanié is nice and concise. Like the Bolton and Dewatripont book suggested by Bayesian (and most other books on this topic) it is pitched at a graduate level and certainly does not fall into the "popular science" category.
The theory of contracts grew out of the failure of the general equilibrium model to account for the strategic interactions among agents that arise from informational asymmetries. This popular text, revised and updated throughout for the second edition, serves as a concise and rigorous introduction to the theory of contracts for graduate students and professional economists. The book presents the main models of the theory of contracts, particularly the basic models of adverse selection, signaling, and moral hazard. It emphasizes the methods used to analyze the models, but also includes brief introductions to many of the applications in different fields of economics. The goal is to give readers the tools to understand the basic models and create their own.