Algebra: Abstract and Concrete by Frederick Goodman
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For a two-semester, undergraduate- level course in Introduction to Modern/Abstract Algebra.
This innovative and versatile text starts by counting symmetries and then quickly gets into group theory. Symmetry (and geometry) is a theme throughout. Author has website as well.
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I. BASICS.
1. Symmetry.II. TOPICS.
9. Field Extensions - Second Look.