Filla, a demon-in-training, meets the angel-in-training
Micael at school and is immediately fascinated by him. When they grow
up, they become partners who work together to guide the souls of the dead
to Heaven. Filla chases after Micael, without much success. Micael has
some problems. He has a lot of guilt because of things that happened in
his past that weren't really his fault, and because of that he doesn't
want to get close to anyone, to risk hurting someone and being hurt.
On top of that, they have the usual problems of angel and demon manga
protagonists, with humans in need of help and worlds in need of saving.
There is a lot more to the story than that, but I don't want to spoil it
for anyone who doesn't want to be spoiled.
I think "Matendou Sonata" is a fantastic manga. It's funny, sweet, and
dramatic, and the ending nearly brought me to tears. It suffers a little
from neon-light foreshadowing, amateurish artwork at the beginning, and
the parts where the author tries to tackle Big Important Issues, where she
comes across (to me, at least) as somewhat shallow and simplistic. But it
was a manga written for middle and high school students, after all. The
characters are loveable, and it is still one of my favorite manga series.
Now, if you want to be spoiled (or you've already read the translations) you can start reading a
detailed plot synopsis which so far covers up to volume 8.