All 4 Uses

nevertheless
in
O Pioneers!
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Nevertheless, when one considered that his chief business was horse-doctoring, it seemed rather short-sighted of him to live in the most inaccessible place he could find.†
Chpt 1.3 *

nevertheless = despite that (used to connect contrasting ideas)
Lou looked anxious, nevertheless.†
Chpt 2.10
Nevertheless, the underground stream was there, and it was because she had so much personality to put into her enterprises and succeeded in putting it into them so completely, that her affairs prospered better than those of her neighbors.†
Chpt 3.2
Nevertheless, he felt that this leave-taking would be more final than his earlier ones had been; that it meant a definite break with his old home and the beginning of something new—he did not know what.†
Chpt 4.3

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)