All 3 Uses

notwithstanding
in
The Merchant of Venice
(Edited)

The man is, notwithstanding, sufficient.
Scene 1.3

notwithstanding = in spite of; or in spite of the thing just mentioned (used to connect contrasting ideas)
Notwithstanding, use your pleasure; if your love do not persuade you to come, let not my letter.
Scene 3.2
ANTONIO: I am the unhappy subject of these quarrels.
PORTIA: Sir, grieve not you; you are welcome notwithstanding.
Scene 5.1 *

notwithstanding = despite what was just said (in this case, even though he is the subject of the quarrels, he is still welcome.)

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)