This book consists of a series of introductory lectures on mirror symmetry and its surrounding topics. These lectures were provided by participants in the PIMS Superschool for Derived Categories and D-branes in July 2016. Together, they form a comprehensive introduction to the field that integrates perspectives from mathematicians and physicists alike. These proceedings provide a pleasant and broad introduction into modern research topics surrounding string theory and mirror symmetry that is approachable to readers new to the subjects. These topics include constructions of various mirror pairs, approaches to mirror symmetry, connections to homological algebra, and physical motivations. Of particular interest is the connection between GLSMs, D-branes, birational geometry, and derived categories, which is explained both from a physical and mathematical perspective. The introductory lectures provided herein highlight many features of this emerging field and give concrete connections between the physics and the math. Mathematical readers will come away with a broader perspective on this field and a bit of physical intuition, while physicists will gain an introductory overview of the developing mathematical realization of physical predictions.

The editors would like to thank the Donner Foundation, the Draeger Foundation, and the Government of Canada for their timely and generous support of this study. The study was initiated by the editors as part of the research program of the Center of Canadian Studies at the Paul H. Nitze School of Advanced International Studies, The Johns Hopkins University, Washington, D.C., and the emerging affiliated program in North American Studies. Particular appreciation goes to Dr. Barbara G. Doran for the final editing of the entire manuscript. In addition to the individuals acknowledged in each of the chapters, the editors thank those scholars who helped guide the project at various times with constructive criticism and discussion: Tom Barnes, Robert Bothwell, Reuven Brenner, David Calleo, Colin Campbell, Benjamin Ginsberg, Judith Goldstein, Peter Katzenstein, Allan Kornberg, Jonathan Lemco, Seymour Martin Lipset, Charles Lipson, Charles Pearson, Richard Rosecrance, and Sidney Weintraub.

This book consists of a series of introductory lectures on mirror symmetry and its surrounding topics. These lectures were provided by participants in the PIMS Superschool for Derived Categories and D-branes in July 2016. Together, they form a comprehensive introduction to the field that integrates perspectives from mathematicians and physicists alike. These proceedings provide a pleasant and broad introduction into modern research topics surrounding string theory and mirror symmetry that is approachable to readers new to the subjects. These topics include constructions of various mirror pairs, approaches to mirror symmetry, connections to homological algebra, and physical motivations. Of particular interest is the connection between GLSMs, D-branes, birational geometry, and derived categories, which is explained both from a physical and mathematical perspective. The introductory lectures provided herein highlight many features of this emerging field and give concrete connections between the physics and the math. Mathematical readers will come away with a broader perspective on this field and a bit of physical intuition, while physicists will gain an introductory overview of the developing mathematical realization of physical predictions.