All 5 Uses

nonetheless
in
The Idiot
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All observed how irritable and cross she had become since her last burst of laughter; but none the less obstinately did she stick to her absurd whim about this new game.†
Chpt 1.13

none the less = in spite of that (used to connect contrasting ideas)
Of course, the worst of it is that, knowing he was a rascal, and a card-sharper, I none the less played palki with him, and risked my last rouble.†
Chpt 2.2 *
But even supposing that your mother is a fool, you are none the less, bound to treat her with humanity.†
Chpt 2.9
Doubtless Lizabetha Prokofievna was considered "eccentric" in society, but she was none the less esteemed: the pity was that she was ceasing to believe in that esteem.†
Chpt 3.1
For the "clever commonplace" person, though he may possibly imagine himself a man of genius and originality, none the less has within his heart the deathless worm of suspicion and doubt; and this doubt sometimes brings a clever man to despair.†
Chpt 4.1

Definitions:

(1) (nonetheless)
in spite of that (Used to connect contrasting ideas. Other synonyms could include words and phrases such as nevertheless, all the same, still, and however.)
(2) (meaning too rare to warrant focus)