In this book we focus on Algebraic Complexity Theory， the study of the intrinsic algorithmic difficulty of algebraic problems within an algebraic model of computation. Motivated by questions of numerical and symbolic computation， this branch of research originated in 1954 when Ostrowski [403] inquired about the optimality of Homer's rule. Algebraic complexity theory grew rapidly and has since become a well-established area of research. However， with the exception of the now classic monograph by Borodin and Munro， published in 1975， a systematic treatment of this theory is not available. .This book is intended to be a comprehensive text which presents both traditional material and recent research in algebraic complexity theory in a coherent way. Requiring only some basic algebra and offering over 350 exercises， it should be well-suited as a textbook for beginners at the graduate level. With its extensive bibliographic notes covering nearly 600 research papers， it might also serve as a reference book. ...
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