From one of the most respected historians in America, twice the winner of the Pulitzer Prize, a new collection of essays that reflects a lifetime of erudition and accomplishments in history. The past has always been elusive: How can we understand people whose worlds were utterly different from our own without imposing our own standards and hindsight? What did things feel like in the moment, when outcomes were uncertain? How can we recover those uncertainties? What kind of imagination goes into the writing of transformative history? Are there latent trends that distinguish the kinds of history we now write? How unique was North America among the far-flung peripheries of the early British empire? As Bernard Bailyn argues in this elegant, deeply informed collection of essays, history always combines approximations based on incomplete data with empathic imagination, interweaving strands of knowledge into a narrative that also explains. This is a stirring and insightful work drawing on the wisdom and perspective of a career spanning more than five decades—a book that will appeal to anyone interested in history.

Algebraic groups and Lie groups are important in most major areas of mathematics, occuring in diverse roles such as the symmetries of differential equations and as central figures in the Langlands program for number theory. In this book, Professor Borel looks at the development of the theory of Lie groups and algebraic groups, highlighting the evolution from the almost purely local theory at the start to the global theory that we know today. As the starting point of this passagefrom local to global, the author takes Lie's theory of local analytic transformation groups and Lie algebras. He then follows the globalization of the process in its two most important frameworks: (transcendental) differential geometry and algebraic geometry. Chapters II to IV are devoted to the former,Chapters V to VIII, to the latter.The essays in the first part of the book survey various proofs of the full reducibility of linear representations of $SL 2M$, the contributions H. Weyl to representation and invariant theory for Lie groups, and conclude with a chapter on E. Cartan's theory of symmetric spaces and Lie groups in the large.The second part of the book starts with Chapter V describing the development of the theory of linear algebraic groups in the 19th century. Many of the main contributions here are due to E. Study, E. Cartan, and above all, to L. Maurer. After being abandoned for nearly 50 years, the theory was revived by Chevalley and Kolchin and then further developed by many others. This is the focus of Chapter VI. The book concludes with two chapters on various aspects of the works of Chevalley on Lie groupsand algebraic groups and Kolchin on algebraic groups and the Galois theory of differential fields.The author brings a unique perspective to this study. As an important developer of some of the modern elements of both the differential geometric and the algebraic geometric sides of the theory, he has a particularly deep appreciation of the underlying mathematics. His lifelong involvement and his historical research in the subject give him a special appreciation of the story of its development.