aunque - indicativo or subjuntivo?
A concessive clause names an obstacle and states that the action happens anyway. The key conjunction is aunque. It covers both although and even if. English picks a different conjunction for each; Spanish keeps aunque and lets the mood of the verb decide.
Same structure, three situations
Aunque llueve, salgo.
Although it's raining, I'm going out.
indicativo – you are telling me it is raining right now
Aunque llueva, saldré.
Even if it rains, I'll go out.
subjuntivo – whether it rains is open
Aunque sea caro, lo compro.
Even though it is expensive, I'll buy it.
subjuntivo – both of you already know it is expensive
por mucho que and por muy ... que
These phrases strengthen the concession (however much). Por mucho que is followed by a verb; por muy by an adjective or adverb, then que and the verb. The verb is normally in the subjuntivo. Por más que means the same as por mucho que.
Por mucho que estudies, es difícil.
However much you study, it stays hard.
Por mucho que lo intentes, no lo conseguirás.
No matter how hard you try, you won't manage it.
Por muy caro que sea, lo necesito.
However expensive it is, I need it.
aun así - even so
Aun así concedes an obstacle without a clause of its own: even so. Here aun has no accent (= even). With an accent, aún means still or yet.
Aun así, lo intentaré.
Even so, I'll try.
Aún no lo he hecho.
I still haven't done it.
