It's possible to go on at great length about this composer and his however-many symphonies (the first is apparently lost, the 16th is more like a concerto, and there are those who would disallow the twelfth). You can find discussions of some of the individual symphonies in the reviews of their respective recordings. What I'd like to do here is try to give you an overview of Pettersson the symphonist and the recordings in this collection.
I'll start by saying that this set is one of the treasures of my CD collection. I also have pretty close to a complete set of all analog LP versions of Pettersson's works, along with a few CDs of individual symphonies. And "individual" really is the word for those symphonies. Pettersson occasionally drops hints of other composers, but he's entirely his own man. An outsider for just about his entire life, he started gaining some proponents in the last few years of his life -- Dorati, Commissiona, Paul Rapoport (critic for Fanfare Magazine). But he is still very much out of the mainstream, and concert performances of his symphonies are exceedingly rare. I've never found one I could attend.
Pettersson did not lead a happy life. He was an orchestral musician until a severe case of rheumatoid arthritis incapacitated him. His temperament was pessimistic, and calling his personality "gruff" or "blunt" is putting a good face on things. His music depicts predominantly struggle and pain. Even so, it's not a downer. I suspect that his pessimism was tempered by the feeling that no matter how bad a hand life might deal him, he would find a way to prevail. Stylistically, the music is quite free. I can't recall a sonata form in any of the symphonies. Its coherence is emotional, rather than structural.
But what does it sound like? It sounds like Pettersson. What else? He uses the orchestra masterfully and frequently masses many instruments into a really powerful sound. Mahler wrote for a huge orchestra but tended to isolate individual instruments or small groups. Pettersson's textures are much thicker, but no less interesting. There is comparatively little forward movement, as such, and much of the time you can't tell where the music is going until after it's arrived. But it's not aleatory or serial; it's just heavily chromatic and loosely structured. Often you'll find the music repeating obsessively or slowly varying, not quite like minimalism but with strong hints of it. You can't fully grasp any of these symphonies in one or two hearings -- or maybe even ten. But you can *feel* them instantly.
What differentiates Pettersson is how emotional his music is. He makes Mahler and Bruckner sound like introverts. If you really focus on the music as it goes by, you may find yourself emotionally shaken long before the symphony ends. If I mak risk a couple of similes, it's like *King Lear* or a Breughel painting. Whether you appreciate this sort of music is up to you. If you do, Pettersson's your man. If you're still unsure, try to find a way to listen to the Seventh or Eighth. They're about as "easy" as Pettersson gets. If you like what you hear, this set's the next step. Then you can consider whether to get other performances of individual symphonies.
As for this set, it doesn't always have the best performances. I won't go into detail, because you can find discussions in posted review of the individual symphonies. I myself prefer Dorati in the Seventh and Commissiona in the Eighth, and there are some others where you really ought to check out the competition. But I'd still get this set first. The price is right, there are no outright failures among the performances, the sound is more than adequate (no easy feat in this music), and several of the symphonies are available only in the versions on this set.
As I said before, I treasure this set. I hope I've helped you a little bit in deciding whether you will, too. Now it's up to you.