All 12 Uses

however
in
The Importance of Being Earnest
(Edited)

However, it makes no matter, for, now that I look at the inscription inside, I find that the thing isn't yours after all.
Act 1

however = a word used to connect contrasting ideas as when using though, in spite of that, in contrast, nevertheless, etc.
However, I am quite ready to enter your name, should your answers be what a really affectionate mother requires.
Act 1
However, that could easily be altered.
Act 1
However, I don't mind hard work where there is no definite object of any kind.
Act 1
However badly he may have behaved to you in the past he is still your brother.
Act 2 *

however = regardless of how
However, you have got to catch the four-five, and I hope you will have a pleasant journey back to town.
Act 2

however = a word used to connect contrasting ideas as when using though, in spite of that, in contrast, nevertheless, etc.
I am not sure, however, that the news inspires me with feelings of unmixed delight.
Act 2
However, I will tell you quite frankly that I have no brother Ernest.
Act 2
I am glad, however, that he made up his mind at the last to some definite course of action, and acted under proper medical advice.
Act 3
My own decision, however, is unalterable.
Act 3
However, as your present mood seems to be one peculiarly secular, I will return to the church at once.
Act 3 *
I did my best, however, though I was out of practice.
Act 3

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?"