Edited by Prog Rock Man - 5/26/10 at 8:50am
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Two classic albums by Tortoise and Tristeza, who are from San Francisco and occupy the, softer more melodic end of the genre.
Nice and educational start, PRM. Thanks!
- Ed
From the harder end of the genre where rhythm and lead guitar dominate in a wall of sound, Germany's Daturah and the US's Russian Circles.
French band Microfilm and a very happy uplifting sound with a rock beat and samples from old film dialogue
Never really understood this Post-Rock label - so help me out.
Are Isis and Mono (Japanese band) following Post Rock or not?
And which Mogwai album should I start off with?
May I submit for Post-Rock...
Godspeed You! Black Emperor's - f♯a♯∞
and Red Sparowes - At The Soundless Dawn
and for Math-Rock...
Battles - EP C/B EP
That will do for now 
F*ck Buttons are my current fave post act. I have loved both their full lengths. Tarot Sport was my favorite album of last year in fact. Also a big Tortoise fan, so there can never be enough love for them.
I would call Isis Post-Metal like Pelican. Some may include Red Sparowes as well. I would put Mono under Post-rock, but they probably wouldn't. Many of these bands shy away from these labels, I can't say I blame them. But when I first started listening to this style of music it helped point me in the right direction. Then it's just down to having a listen and seeing what you like.
As far as Mogwai goes, you're spoilt for choice. Rock Action, Come on Die Young and Young Team are all good places to start IMO.
Have you got links to Isis and Mono, there are other bands which share the name?
As for Mogwai, my first album was Rock Action, but all of their albums have their distinct sound. If you like that try Explosions in The Sky
and from Sheffield in England the rather intense 65daysofstatic for the darker side of post rock.
I assume Jubie is referring to this ISIS...
http://www.discogs.com/artist/Isis+(6)
Of whom Oceanic and Panopticon are damn good albums
I generally don't then to bother too much about genre labels (especially sub-genre labels), but was curious enough since every now and then people talk about Post-Rock and I have no idea what they are referring to.
Isis
Mono
Re the genre issue, I want it to be a wide definition and this thread is more about the bands and music, most of whom get very little exposure.
Explosions in the Sky - The Earth is not a Cold Dead Place is my favorite Post-Rock album ever! But I have about 33gb of post rock alone and its hard to talk about it all, but everyone should listen to that album.