(WSP, 2004)(T) This book is conceived as an advanced textbook - suitable for graduate students, interested non-experts, and even ambitious undergraduates - to provide a broad introduction to the subject of exactly solved quantum many-body systems. These systems are necessarily one-dimensional, but should that change in the future, I will happily include higher-dimensional examples in a new edition of this book! As the subtitle indicates, the topic began more than 70 years ago - soon after the invention of quantum mechanics - and has been steadily growing since. My only ambition for the book is to provide a largely self-contained presentation - as broad and coherent as feasible - that will interest the interested reader, and provide the background necessary should that wish to go further and enter the vast and intimidating research literature. Oh yes, and with a minimum of mistakes.