What are these stone's circles?

chances are, these are fossil corals or some other reef buidler .The rock had been broken off its "ledge" and then tumbled in a stream or dumped around by a glacier.
We have similar stones in the upper Peninsula of Michigan, We call em "Petoskey STones" after the county in which theyre found.
Such kinds of rocks /fossis are found all over the world (usually we see them along beaches and in river beds

However, since the rock is quartzite, it could be a bunch of quartz crystal vugs that were broken off the outcrop.
Look closely and see whether you can see a mineral like internal structure (crystals or laminae) or actual biological features like youd perhaps see in early corals.

I found this stone in a mountain, while I was photographing the breccias. The place is relatively far from the sea. So it might be possible for it to have formed part of the bottom of the sea at some time in the past. The stone is very lightly magnetic. For me it has biological features, like a bony and porous appearance inside the cells.

If you could make some better (close up) pictures of the round segments (ALso put a die or a nickel next to it, and in the view field, for scale). I can probably identify the speies of "rudist" corals or whatnot. Im just a bit confused because it looks like its a quartz rock.
Also, its obviously been rounded by a stream or glacier

PS, the breccia was quite neat. Are you a student or a hobbyist?

I read that fossils in regions surrounded by metamorphic rocks are very rare, so it could be possible for the stone to not be a fossil after all. I took another set with a quarter dollar coin as scale, by the way, flicker photos are displayed in smaller sizes by default, you can click over them, and then click view all sizes in the upper-most right corner, to pick up the larger one. If you have done so, then these are the best photos I can take with my camera, sorry for that. I hope you can identify what are the circles at all. I thank you very much in advance. I am just a hobbyist, I have always wanted to know what were that old looking rocks. Thank you. New set: http://www.flickr.com/photos/51986587@N04/sets/72157632701484395/

If the round circles are biological fossils, then what you might have is a fossilized sponge, or maybe some tube worms.

It would help if we knew the approximate age of the rocks and where they were found, both geographically and in the strata.

Fossils in metamorphic rockss are aalways stretched and mangled a bit, or else they are marked by ultr temperatures. SO I think were dealing with a sedimentary rock that has been rolled around and polished (DID you say this rock ws found nar the mountins? In a very dry environment? If thats the case, the rounding and brown "polished " look could be what we call " desert varnish"

Im stickin with brachiopods , especially thoe from Devonian rocks.

Indeed, I found the rock while walking over a mountain, the rock was loose over the soil, I didn't dig up a centimeter. The mountainous region is semi desertic, not extremely dry, but indeed, very dry. Other guys agreed with you in identifying the fossil as brachiopods. So I will stick to this identification.