This book provides an introduction to topological groups and the structure theory of locally compact abelian groups, with a special emphasis on Pontryagin-van Kampen duality, including a completely self-contained elementary proof of the duality theorem. Further related topics and applications are treated in separate chapters and in the appendix.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

Italian astronomer and Dominican friar Giordano Bruno (1548–1600), found guilty of heresy by the Roman Inquisition and burned at the stake, has long been an enigma of early modern European philosophy. His central 1586 work On the Heroic Frenzies has shown a particular need for a fresh examination. This vibrant bilingual edition, annotated by celebrated Bruno scholar Ingrid D. Rowland, features the text in its original Italian alongside an elegant, accurate English translation. On the Heroic Frenzies is at once a philosophical dialogue, an anthology of love poetry, and a collection of sonnets, songs, and emblems – sometimes borrowed from other writers, but primarily Bruno’s own. Rowland’s detailed introduction and extensive footnotes highlight the philosophical sources, Biblical allusions, and biographical elements that make Bruno’s work both richly conceived and often challenging to understand. Providing cohesive insights into Bruno’s text, Rowland’s edition of On the Heroic Frenzies is a helpful guide for those new to his work.

Giordano Bruno’s Cabala del cavallo pegaseo (The Cabala of Pegasus) grew out of the great Italian philosopher’s experiences lecturing and debating at Oxford in early 1584. Having received a cold reception there because of his viewpoints, Bruno went on in the Cabala to attack the narrow-mindedness of the university--and by extension, all universities that resisted his advocacy of intellectual freethinking. The Cabala of Pegasus consists of vernacular dialogues that turn on the identification of the noble Pegasus (the spirit of poetry) and the humble ass (the vehicle of divine revelation). In the interplay of these ideas, Bruno explores the nature of poetry, divine authority, secular learning, and Pythagorean metempsychosis, which had great influence on James Joyce and many other writers and artists from the Renaissance to the modern period. This book, the first English translation of The Cabala of Pegasus, contains both the English and Italian versions as well as helpful annotations. It will have particular appeal to all Renaissance scholars and those interested in the Renaissance cabalistic underpinnings of modern literature.

Giordano Bruno's The Ash Wednesday Supper is the first of six philosophical dialogues in Italian that he wrote and published in London between 1584 and 1585. It presents a revolutionary cosmology founded on the new Copernican astronomy that Bruno extends to infinite dimensions, filling it with an endless number of planetary systems. As well as opening up the traditional closed universe and reducing earth to a tiny speck in an overwhelmingly immense cosmos, Bruno offers a lively description of his clash of opinions with the conservative academics and theologians he argued with in Oxford and London. This volume, containing what has recently been claimed as the final version of Bruno's Ash Wednesday Supper, presents a new translation based on a newly edited text, with critical comment that takes account of the most current discussion of the textual, historical, cosmological and philosophical issues raised in this dialogue. It considers Bruno's work as a seminal text of the late European renaissance.