All 3 Uses of

however
in
The Iliad by Homer - (translated by: Edward)

Such I believe to be the true interpretation of this passage, which, however, is one of admitted difficulty.†
Chpt Foot *

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

The King being obliged to send back his captive, enters into a furious contest with Achilles, which Nestor pacifies; however, as he had the absolute command of the army, he seizes on Briseis in revenge.†
Chpt 1.1

The terms made use of in this line, and in 481, may appear somewhat coarse, as addressed by one Goddess to another: but I assure the English reader that in this passage especially I have greatly softened down the expression of the original; a literal translation of which, however forcible, would shock even the least fastidious critic.†
Chpt Foot

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 contrastand 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)
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?"