This book provides a detailed and largely self-contained description of various classical and new results on solvability and unsolvability of equations in explicit form. In particular, a complete exposition of topological Galois theory is given. This theory is due to the author. Applications of Galois theory to solvability of algebraic equations by radicals, basics of the Picard-Vessiot theory, Liouville's results on the class of functions representable by quadratures are also discussed.
A unique feature of this book is that recent results are presented in the same elementary manner as classical Galois theory. Due to this feature, the book will be useful and interesting to readers with very different background in mathematics, from undergraduate students to researchers.
Askold Khovanskii is a Professor of Mathematics at the University of Toronto, and a principal researcher at the RAS Institute for Systems Analysis (Moscow, Russia). He is a founder of topological Galois theory and the author of fundamental results in this area.
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