The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to continue your study of abstract algebra be learning about rings, fields, modules and vector spaces.
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We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Editionhttp://amzn.to/2oOBd5S
Milne, Algebra Course Notes (available free online)http://www.jmilne.org/math/CourseNotes/index.html
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