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The Boston College Math Case Studies Project was developed to help prepare graduate students in mathematics to be teaching assistants and instructors of courses. Such beginning teachers will face a myriad of challenges in their teaching roles and the case studies were developed to explore some of these challenges. Each case study gives a fictional scenario in which a graduate student is faced with a multi-faceted problem. Problems in the cases include possible cheating on an exam, an aggressive student seeking additional points on an exam, the sudden realization that most students learned little from the previous lecture, dealing with struggling students, the effective use of technology, and handling a class of varied abilities. The case studies were written to give a balance of views, with no simple solutions. As such, they give graduate students the opportunity to articulate and hear a variety of viewpoints and approaches. They also give a safe environment in which to face potential challenges and explore possible solutions. The case studies were developed by a team led by Sol Friedberg (Boston College). We describe the case studies more fully and report on their use as part of the training of beginning graduate instructors at Boston College.