All 7 Uses

nevertheless
in
The ABC Murders
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"Nevertheless," continued Poirot, "in view of what has happened, the police there would like to have another look at the anonymous letter I received.†
Chpt 3

nevertheless = despite that (used to connect contrasting ideas)
Nevertheless I felt convinced that something ought to be done and that we should not allow the grass to grow under our feet.†
Chpt 8 *
But her eye brightened nevertheless.†
Chpt 9
"Nevertheless, my friend," said Poirot, looking straight at him, "it is there in those questions that the solution lies.†
Chpt 13
Nevertheless, there must exist indications which are not vague but certain.†
Chpt 18
Nevertheless, by the end of the day, I had at any rate an idea as to the direction in which Poirot's thoughts were tending.†
Chpt 32
Nevertheless, there was a very real danger that on the death of your sister-in-law he might, in his loneliness, turn to this beautiful girl for sympathy and comfort and it might end-as so often happens with elderly men-in his marrying her.†
Chpt 34

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)