Fact or possibility: obwohl against auch wenn
A concessive says: this would normally stop it, and it did not. obwohl concedes something that is true. auch wenn and selbst wenn discount something that may or may not happen. English even though against even if is the best guide. All three send the verb to the end.
Obwohl ich müde war, bin ich noch mitgekommen.
Even though I was tired, I still came along.
I was tired: a fact
Auch wenn es morgen schneit, fahren wir los.
Even if it snows tomorrow, we're setting off.
it may or may not snow
Selbst wenn du dich entschuldigst, ändert das nichts.
Even if you apologise, it doesn't change anything.
selbst wenn is the stronger of the two
auch wenn can also be used about facts, like obwohl: Auch wenn es regnet, gehen wir spazieren can mean although it is raining. Only the situation tells you which. obwohl, however, is never hypothetical. The safe route: obwohl for facts, selbst wenn for possibilities.
zwar … aber: the balanced concession
zwar means roughly admittedly. Both halves are main clauses with the verb in second position, and aber (or doch) sits outside the clause and changes nothing. zwar usually stands inside the clause after the verb. At the start of the sentence it is more formal, and the subject moves behind the verb. A listener who hears zwar is waiting for the aber.
Das Essen war zwar gut, aber der Service war schrecklich.
The food was good, admittedly, but the service was terrible.
Zwar kenne ich ihn kaum, aber er wirkt sympathisch.
True, I hardly know him, but he seems likeable.
zwar first: verb second, subject third
Er hat zwar zugesagt, doch gekommen ist er nicht.
He did say yes, but he never turned up.
doch instead of aber: a touch more literary
The formal end of the range
Three more patterns, at home in writing. You need them mostly to read, but a well-placed wenngleich is worth several ordinary sentences.
wenngleich, wenn auch
More formal synonyms of obwohl. wenngleich introduces a clause with the verb at the end. wenn auch can do the same, or be followed by a single word or phrase.
Die Zahlen sind gut, wenngleich sie hinter der Prognose zurückbleiben.
The figures are good, albeit below forecast.
Das Essen war gut, wenn auch etwas teuer.
The food was good, if a little expensive.
dennoch, gleichwohl
Formal adverbs that work like trotzdem: first position, verb straight after.
Der Antrag kam zu spät. Dennoch wurde er bearbeitet.
The application arrived late. It was processed nonetheless.
wer / was / wie auch immer
The -ever words are built from a question word plus auch immer. The clause has the verb at the end.
Ich stehe hinter dir, was auch immer du entscheidest.
I'm behind you, whatever you decide.
Ich gehe nicht ran, wer auch immer anruft.
I'm not picking up, whoever calls.