Although: mặc dù / tuy … nhưng

Mặc dù means "although". When it opens the sentence, the second half usually starts with nhưng, which English would drop, and has vẫn (still) or cũng before the verb: Mặc dù trời mưa nhưng quán vẫn đông. Although it's raining, the place is still busy. Nhưng can be left out, but vẫn or cũng usually stays: Mặc dù mệt, em vẫn đi làm.

Tuy means the same and sounds a little more careful: Tuy lương không cao nhưng em thích công việc này. Although the pay isn't great, I like this job.

The mặc dù part can also come second, as an afterthought, and then there's no nhưng: Em vẫn đi học, mặc dù hơi mệt.

In relaxed speech you don't always need "although" at all: Mệt nhưng em vẫn đi làm says the same. For "even if", about something that may or may not happen, use dù … cũng. And in writing, a new sentence starting with Tuy nhiên means "however".