A rigorous treatment of a thought experiment that has become notorious within and outside of philosophy - The Trolley Problem - by one of the most influential moral philosophers alive today.Suppose you can stop a trolley from killing five people, but only by turning it onto a side track where it will kill one. May you turn the trolley? What if the only way to rescue the five is to topple a bystander in front of the trolley so that his body stops it but he dies? May you use a device tostop the trolley that will kill a bystander as a side effect? The "Trolley Problem" challenges us to explain and justify our different intuitive judgments about these and related cases and has spawned a huge literature. F.M. Kamm's 2013 Tanner Lectures present some of her views on this notoriousmoral conundrum. After providing a brief history of changing views of what the problem is about and attempts to solve it, she focuses on two prominent issues: Does who turns the trolley and how the harm is shifted affect the moral permissibility of acting? The answers to these questions lead togeneral proposals about when we may and may not harm some to help others. Three distinguished philosophers - Judith Jarvis Thomson (one of the originators of the trolley problem), Thomas Hurka, and Shelly Kagan - then comment on Kamm's proposals. She responds to each comment at length, providing an exceptionally rich elaboration and defense of her views. The TrolleyProblem Mysteries is an invaluable resource not only to philosophers concerned about the Trolley Problem, but to anyone worried about how we ought to act when we can lessen harm to some by harming others and how we can reach a decision about the question.