The first part of this book provides an elementary and
self-contained exposition of classical Galois theory and its
applications to the questions of solvability of algebraic equations
in explicit form. The second part describes a surprising analogy
between the fundamental theorem of Galois theory and classification
of coverings over a topological space. The third part contains a
geometric description of finite algebraic extensions of the field
of meromorphic functions on a Riemann surface and provides an
introduction to topological Galois theory developed by the author.
All results are presented in the same elementary and self-contained
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.
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