All 4 Uses

however
in
The Nose, by Gogol
(Edited)

Instead, however, of going to shave any officials, he turned his steps to a building, the sign-board of which bore the legend "Teas served here," in order to have a glass of punch, when suddenly he perceived at the other end of the bridge a police inspector of imposing exterior, with long whiskers, three-cornered hat, and sword hanging at his side.

however = a word used to connect contrasting ideas as when using though, in spite of that, in contrast, nevertheless, etc.
"However, if you lay so much stress on it, you should apply to someone who has a skilful pen, so that he may describe it as a curious, natural freak, and publish the article in the Northern Bee" (here he took another pinch) "for the benefit of youthful readers" (he wiped his nose), "or simply as a matter worthy of arousing public curiosity."
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But however often he tried, all his efforts were in vain.
*

however = regardless of how
At last he began to pass the razor very lightly over the Major's chin, and although it was very difficult to shave him without using the olfactory organ as a point of support, he succeeded, however, by placing his wrinkled thumb against the Major's lower jaw and cheek, thus overcoming all obstacles and bringing his task to a safe conclusion.

however = a word used to connect contrasting ideas as when using though, in spite of that, in contrast, nevertheless, etc.

Definitions:

(1) (however as in: However, complications may...)
though (or another expression that connects contrasting ideas)

Based on idea 1 we might not expect idea 2, but this is a way of saying that even though idea 1 exists, we still have idea 2. Synonyms include in spite of that, despite that, nevertheless, nonetheless, on the other hand, in contrast and but.
(2) (however as in: However much she tried...)
to whatever degree (regardless of how much; or whatever unspecified amount)
(3) (however as in: However you do it, get it done!)
in whatever way
(4) (meaning too rare to warrant focus)
Much more rarely (and arguably incorrectly), however can be used to intensify the word how, as when one says "However did you find her?" Grammarians would suggest using two words for that usage: "How ever did you find her?"