Both Uses

nevertheless
in
Crime and Punishment, by Dostoyevsky
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"Love for the future partner of your life, for your husband, ought to outweigh your love for your brother," he pronounced sententiously, "and in any case I cannot be put on the same level....Although I said so emphatically that I would not speak openly in your brother's presence, nevertheless, I intend now to ask your honoured mother for a necessary explanation on a point of great importance closely affecting my dignity.†
Chpt 4.2

nevertheless = despite that (used to connect contrasting ideas)
But, nevertheless, it was clear to him again that with her character and the amount of education she had after all received, she could not in any case remain so.†
Chpt 4.4 *

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)