Galois idea is among the most pretty branches of arithmetic. by means of synthesising the concepts of workforce conception and box thought it offers an entire solution to the matter of the solubility of polynomials by way of radicals: that's, the matter of selecting whilst and the way a polynomial equation could be solved through time and again extracting roots and utilizing common algebraic operations. This textbook, in response to lectures given over a interval of years at Cambridge, is an in depth and thorough creation to the topic. The paintings starts with an effortless dialogue of teams, fields and vector areas, after which leads the reader via such issues as jewelry, extension fields, ruler-and-compass structures, to automorphisms and the Galois correspondence. by means of those ability, the matter of the solubility of polynomials via radicals is replied; particularly it's proven that no longer each quintic equation may be solved through radicals. all through, Dr Garling offers the topic no longer as whatever closed, yet as one with many functions. within the ultimate chapters, he discusses additional issues, akin to transcendence and the calculation of Galois teams, which point out that there are various questions nonetheless to be spoke back. The reader is thought to haven't any prior wisdom of Galois conception. a few event of recent algebra is useful, in order that the booklet is appropriate for undergraduates of their moment or ultimate years. There are over 2 hundred workouts which offer a stimulating problem to the reader.