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The field of astrophysics is in the midst of a technologically driven renaissance, as fundamental discoveries are being made with astonishing frequency. In the last decade, new detectors in space, on earth, and deep underground have, when coupled with the computational power of modern computers, revolutionized our knowledge and understanding of the astronomical world. This is a great time for a student of any age to become acquainted with the remarkable universe in which we live. This volume is a collection of essays, originally presented orally to a diverse group of students and professionals, which reveal the most fertile areas for future study of astronomy and astrophysics. The emphasis of this work is on the clear description of the current state of our knowledge as a preparation for the future unraveling of the mysteries of the universe that appear today as most fundamental and most amenable to solution. A stellar group of astronomers and astrophysicists describes the directions and styles of work that they think are most likely to lead to progress. Bibliographical notes at the end of each presentation provide guidance for the reader who wishes to go more deeply into a given subject. Unsolved Problems in Astrophysics is a uniquely stimulating introduction to some of the most important topics in modern astrophysics.