Bakunin's theory of anarchy, in two words, is "the order arises from the anarchy, as people decide, what's best for them". But again, that's two words, and these can easily be understood in a very wrong way. So, some serious reading is required here for proper understanding.
Anarchy is not some man-eat-man thing, it's about freedom from any supreme power above the basic and independent communes of free people.
ADD-ON: As to your question about the communist party back here, it's really sold out ATM. They wear all those nice 5000$ suits, swiss watches and talk of "the people's rage", "endorse social justice" (like hell they are!). They sold the great country to the cunts. I'm not saying SU was perfect, as I took a share of it, but it definitely wasn't nearly as bad, as it is portrayed, in its late years that is. It could surely have undergone some renaissance, instead of just ruining it all to hell, and bringing us to the caveman age all at once.