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These are notes to pp. 1-11 and 21-49 of Artin’s classic—”the last corrected printing of the 1944 second revised edition,” republished by Dover in 1998—to assist the study of his account of Galois theory as far as the Fundamental Theorem. In some places I have followed Artin’s revised German edition (Teubner, 1959), which seems not to have been translated into English. I hope that any mistakes that may be noticed will be brought to my attention.

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This is a version of an elementary lecture I gave recently. At the end some questions raised or implied but not answered in the lecture are posed as exercises; these are cited along the way as Q1, Q2, etc. Some of them are less gentle than the lecture.

If symbols are not legible, refreshing the page usually restores them.

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