All 5 Uses

nevertheless
in
The Brothers Karamazov
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"Nevertheless I would rather bite out my tongue than be lacking in respect to the sainted man whom you reverence so highly," he wrote in conclusion.†
Chpt 1 *

nevertheless = despite that (used to connect contrasting ideas)
Nevertheless, it was particularly unpleasant to him to meet certain persons, whose presence aroused in him great misgivings.†
Chpt 7
Nevertheless, he went to see Mitya ten days before the trial and proposed to him a plan of escape—a plan he had obviously thought over a long time.†
Chpt 11
I cannot answer such questions; nevertheless they are disturbing, and every citizen not only must, but ought to be harassed by them.†
Chpt 12
"Nevertheless I venture to suggest," Fetyukovitch continued, "that in spite of his independent mind and just character, my opponent may have formed a mistaken prejudice against my unfortunate client.†
Chpt 12

Definitions:

(1) (nevertheless)
despite that

Based on idea 1 we might not expect idea 2, but this is a way of saying that even though idea 1 was just stated, we still have idea 2. Synonyms include in spite of that, despite that, nevertheless, nonetheless, on the other hand, in contrast and but.
(2) (meaning too rare to warrant focus)