These concepts are useful to "some people", perhaps not to you. Halmos' book on vector spaces is regarded by some as a "classic", he had a reputation as an excellent text-writer.
Permutations can be expressed various ways: as bijective functions of a finite set, as "re-arragements" of a set of letters, or seating arrangements, etc., as a certain kind of group which acts on a set, as certain sets of matrices (which come about by "jumbling" the columns of the identity matrix). The approach taken can make permutations seem like quite different animals, but there are certain facts about them which are true "no matter how we express them".
If you find Halmos' style of exposition (or mine, for that matter) not to your liking, that is your perogative. I do note in passing that the Levi-Civita symbol is a kind of shorthand, and it might be an interesting question to ask: short-hand for what, exactly?