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Our only-partly-done guided tour for beginners goes over the basic definitions of groups, subgroups, cosets, basic results such as Lagrange's theorem, and a little more, along with stimulating exercises. A more complete version of the guided tour will contain all the material covered in a standard undergraduate group theory course.
Our basic definitions in group theory page, that links to most of the basic terms you see in an undergraduate group theory course. There's much much more in the wiki!
Our pages on symmetric group:S3 (see also subgroups, elements, and representations), symmetric group:S4 ((see also subgroups, elements, and representations), symmetric group:S5, dihedral group:D8, quaternion group, alternating group:A4, alternating group:A5, and many more. Well-organized, easily digestible, detailed information.