This third edition is addressed to the mathematician or graduate student of mathematics - or even the well-prepared undergraduate - who would like, with a minimum of background and preparation, to understand some of the beautiful results at the heart of nonlinear analysis. Based on carefully-expounded ideas from several branches of topology, and illustrated by a wealth of figures that attest to the geometric nature of the exposition, the book will be of immense help in providing its readers with an understanding of the mathematics of the nonlinear phenomena that characterize our real world. Included in this new edition are several new chapters that present the fixed point index and its applications. The exposition and mathematical content is improved throughout. This book is ideal for self-study for mathematicians and students interested in such areas of geometric and algebraic topology, functional analysis, differential equations, and applied mathematics. It is a sharply focused and highly readable view of nonlinear analysis by a practicing topologist who has seen a clear path to understanding. "For the topology-minded reader, the book indeed has a lot to offer: written in a very personal, eloquent and instructive style it makes one of the highlights of nonlinear analysis accessible to a wide audience."-Monatshefte fur Mathematik (2006)

Fixed point theory concerns itself with a very simple, and basic, mathematical setting. For a functionf that has a setX as bothdomain and range, a ?xed point off isa pointx ofX for whichf(x)=x. Two fundamental theorems concerning ?xed points are those of Banach and of Brouwer. In Banach's theorem, X is a complete metric space with metricd andf:X?X is required to be a contraction, that is, there must existL< 1 such thatd(f(x),f(y))?Ld(x,y) for allx,y?X. Theconclusion is thatf has a ?xed point, in fact exactly one of them. Brouwer'stheorem requiresX to betheclosed unit ball in a Euclidean space and f:X?X to be a map, that is, a continuous function. Again we can conclude that f has a ?xed point. But in this case the set of?xed points need not be a single point, in fact every closed nonempty subset of the unit ball is the ?xed point set for some map. ThemetriconX in Banach'stheorem is used in the crucialhypothesis about the function, that it is a contraction. The unit ball in Euclidean space is also metric, and the metric topology determines the continuity of the function, but the focus of Brouwer's theorem is on topological characteristics of the unit ball, in particular that it is a contractible ?nite polyhedron. The theorems of Banach and Brouwer illustrate the di?erence between the two principal branches of ?xed point theory: metric ?xed point theory and topological ?xed point theory.

"The book is highly recommended as a text for an introductory course in nonlinear analysis and bifurcation theory... reading is fluid and very pleasant... style is informal but far from being imprecise." -review of the first edition. New to this edition: additional applications of the theory and techniques, as well as several new proofs. This book is ideal for self-study for mathematicians and students interested in geometric and algebraic topology, functional analysis, differential equations, and applied mathematics.

This edition makes available an entirely new version of Hegel's lectures on the development and scope of world history. Volume I presents Hegel's surviving manuscripts of his introduction to the lectures and the full transcription of the first series of lectures (1822-23). These works treat the core of human history as the inexorable advance towards the establishment of a political state with just institutions-a state that consists of individuals with a free and fully-developed self-consciousness. Hegel interweaves major themes of spirit and culture-including social life, political systems, commerce, art and architecture, religion, and philosophy-with an historical account of peoples, dates, and events. Following spirit's quest for self-realization, the lectures presented here offer an imaginative voyage around the world, from the paternalistic, static realm of China to the cultural traditions of India; the vast but flawed political organization of the Persian Empire to Egypt and then the Orient; and the birth of freedom in the West to the Christian revelation of free political institutions emerging in the medieval and modern Germanic world. Brown and Hodgson's new translation is an essential resource for the English reader, and provides a fascinating account of the world as it was conceived by one of history's most influential philosophers. The Editorial Introduction surveys the history of the texts and provides an analytic summary of them, and editorial footnotes introduce readers to Hegel's many sources and allusions. For the first time an edition is made available that permits critical scholarly study, and translates to the needs of the general reader.

Ferdinand Christian Baur (1792-1860) has been described as "the greatest and at the same time the most controversial theologian in German Protestant theology since Schleiermacher." The controversy was epitomized by a nineteenth-century British critic who wrote that his theory "makes of Christianity a thing of purely natural origin, calls in question the authenticity of all but a few of the New Testament books, and makes the whole collection contain not a harmonious system of divine truth, but a confused mass of merely human and contradictory opinions as to the nature of the Christian religion." The contributors to this volume, however, regard Baur as an epoch-making New Testament scholar whose methods and conclusions, though superseded, have been mostly affirmed during the century and a half since his death. This collection focuses on the history of early Christianity, although as a historian of the church and theology Baur covered the entire field up to own time. He combined the most exacting historical research with a theological interpretation of history influenced by Kant, Schelling, and Hegel. The first three chapters discuss Baur's relation to Strauss, Moehler, and Hegel. Then a central core of chapters considers his historical and exegetical perspectives (Judaism and Hellenism, Gnosticism, New Testament introduction and theology, the Pauline epistles, the Synoptic Gospels, John, the critique of miracle, and the combination of absoluteness and relativity). The final chapters view his influence by analyzing the reception of Baur in Britain, Baur and Harnack, and Baur and practical theology. This work offers a multi-faceted picture of his thinking, which will stimulate contemporary discussion.

This edition makes available an entirely new version of Hegel's lectures on the development and scope of world history. Volume I presents Hegel's surviving manuscripts of his introduction to the lectures and the full transcription of the first series of lectures (1822-23). These works treat the core of human history as the inexorable advance towards the establishment of a political state with just institutions-a state that consists of individuals with a free and fully-developed self-consciousness. Hegel interweaves major themes of spirit and culture-including social life, political systems, commerce, art and architecture, religion, and philosophy-with an historical account of peoples, dates, and events. Following spirit's quest for self-realization, the lectures presented here offer an imaginative voyage around the world, from the paternalistic, static realm of China to the cultural traditions of India; the vast but flawed political organization of the Persian Empire to Egypt and then the Orient; and the birth of freedom in the West to the Christian revelation of free political institutions emerging in the medieval and modern Germanic world.
Brown and Hodgson's new translation is an essential resource for the English reader, and provides a fascinating account of the world as it was conceived by one of history's most influential philosophers. The Editorial Introduction surveys the history of the texts and provides an analytic summary of them, and editorial footnotes introduce readers to Hegel's many sources and allusions. For the first time an edition is made available that permits critical scholarly study, and translates to the needs of the general reader.

The Hegel Lectures Series Series Editor: Peter C. Hodgson Hegel's lectures have had as great a historical impact as the works he himself published. Important elements of his system are elaborated only in the lectures, especially those given in Berlin during the last decade of his life. The original editors conflated materials from different sources and dates, obscuring the development and logic of Hegel's thought. The Hegel Lectures series is based on a selection of extant and recently discovered transcripts and manuscripts. The original lecture series are reconstructed so that the structure of Hegel's argument can be followed. Each volume presents an accurate new translation accompanied by an editorial introduction and annotations on the text, which make possible the identification of Hegel's many allusions and sources. Hegel's interpretation of the history of philosophy not only played a central role in the shaping of his own thought, but also has had a great influence on the development of historical thinking. In his own view the study of the history of philosophy is the study of philosophy itself. This explains why such a large proportion of his lectures, from 1805 to 1831, the year of his death, were about history of philosophy. The text of these lectures, presented here in the first authoritative English edition, is therefore a document of the greatest importance in the development of Western thought: they constitute the very first comprehensive history of philosophy that treats philosophy itself as undergoing genuine historical development. And they are crucial for understanding Hegel's own systematic works such as the Phenomenology, the Logic, and the Encyclopedia, for central to his thought is the theme of spirit as engaged in self-realization through the processes of historical change. Furthermore, they played a crucial role in one of the determining events of modern intellectual history: the rise of a new consciousness of human life, culture, and intellect as historical in nature. This third volume of the lectures covers the medieval and modern periods, and includes fascinating discussion of scholastic, Renaissance, and Reformation philosophy, and of such great modern thinkers as Descartes, Locke, Leibniz, and especially Kant.

The Hegel Lectures Series Series Editor: Peter C. Hodgson Hegel's lectures have had as great a historical impact as the works he himself published. Important elements of his system are elaborated only in the lectures, especially those given in Berlin during the last decade of his life. The original editors conflated materials from different sources and dates, obscuring the development and logic of Hegel's thought. The Hegel Lectures series is based on a selection of extant and recently discovered transcripts and manuscripts. The original lecture series are reconstructed so that the structure of Hegel's argument can be followed. Each volume presents an accurate new translation accompanied by an editorial introduction and annotations on the text, which make possible the identification of Hegel's many allusions and sources. This new edition of Hegel's Lectures on the History of Philosophy sets forth clearly, for the first time for the English reader, what Hegel actually said. These lectures challenged the antiquarianism of Hegel's contemporaries by boldly contending that the history of philosophy is itself philosophy, not just history. It portrays the journey of reason or spirit through time, as reason or spirit comes in stages to its full development and self-conscious existence, through the successive products of human intellect and activity. These lectures proved to be extremely influential on the intellectual history of the past two centuries. They are crucial to understanding Hegel's own systematic philosophy in its constructive aspect, as well as his views on the centrality of reason in human history and culture. Volume I holds additional importance because, as well as setting out Hegel's discussion of the history of Chinese and Indian philosophy, it presents the interesting and significant changes that Hegel made to the stage-setting introduction to these lectures across the years from 1819 to 1831. This edition adapts the considerable editorial resources of the German edition that it translates, to the needs of the general reader as well as the serious scholar, so as to constitute an unparalleled resource on this topic in the English language.

The Hegel Lectures Series Series Editor: Peter C. Hodgson Hegel's lectures have had as great a historical impact as the works he himself published. Important elements of his system are elaborated only in the lectures, especially those given in Berlin during the last decade of his life. The original editors conflated materials from different sources and dates, obscuring the development and logic of Hegel's thought. The Hegel Lectures series is based on a selection of extant and recently discovered transcripts and manuscripts. The original lecture series are reconstructed so that the structure of Hegel's argument can be followed. Each volume presents an accurate new translation accompanied by an editorial introduction and annotations on the text, which make possible the identification of Hegel's many allusions and sources. Lectures on the History of Philosophy Volume II: Greek Philosophy Hegel's Lectures on the History of Philosophy offer one of the best points of entry to his philosophical system. The second volume (dating from 1825-6) covers a thousand years of ancient Greek philosophy; this is the period to which Hegel devoted by far the most attention, and which he saw as absolutely fundamental for all that came after it. This edition sets forth clearly, and for the first time for the English reader, what Hegel actually said. It forms part of OUP's Hegel Lectures series, presenting accurate new translations accompanied by editorial introductions and annotations. These lectures challenged the antiquarianism of Hegel's contemporaries by boldly contending that the history of philosophy is itself philosophy, not just history. It portrays the journey of reason or spirit through time, as reason or spirit comes in stages to its full development and self-conscious existence, through the successive products of human intellect and activity. Hegel's Lectures on the History of Philosophy proved to be extremely influential on the intellectual history of the past two centuries. These lectures are crucial to understanding Hegel's own systematic philosophy in its constructive aspect, as well as his views on the centrality of reason in human history and culture. The volume on Greek Philosophy covers the first one thousand years, the period to which Hegel devoted by far the most attention, and which he saw as absolutely fundamental for all that came after it. This edition adapts the considerable editorial resources of the German edition that it translates, to the needs of the general reader as well as the serious scholar, so as to constitute an unparalleled resource on this topic in the English language.