All 4 Uses

notwithstanding
in
The House of the Seven Gables
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When the sound subsided, the silence through the house was deep, dreary, and oppressive, notwithstanding that the tongues of many of the guests had already been loosened by a surreptitious cup or two of wine or spirits.†
Chpt 1
The expression of his countenance—while, notwithstanding it had the light of reason in it—seemed to waver, and glimmer, and nearly to die away, and feebly to recover itself again.†
Chpt 7 *
They are welcome, notwithstanding!†
Chpt 14
Notwithstanding what he had just said, and most sincerely, in regard to the self-balancing power with which Phoebe impressed him, it still seemed almost wicked to bring the awful secret of yesterday to her knowledge.†
Chpt 20

Definitions:

(1) (notwithstanding)
used to show that something remains true even though something else seems to go against it

Most commonly, you can substitute "in spite of" for notwithstanding. But see the first exemplary sample sentences for other common word substitutions.
(2) (meaning too rare to warrant focus)