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Basic definitions in group theory page. There's much much more in the wiki!
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.
Incomplete (not fully finished) guided tour for beginners; the part prepared so far goes over the basic definitions of groups, subgroups, cosets, basic results such as Lagrange's theorem, and a little more, along with stimulating exercises.