I need to learn Kasparov's KK theory but the original paper is written in Russian.
G.G. KASPAROV, The operator K-functor and extensions of C*-algebras, Izv. Akad. Nauk SSSR, Ser. Mat. 44 (1980), 571-636 Math. USSR Izv. 16 (1981), 513-572.
Does anyone know where I can find it's English version?
Try
Mathematics of the USSR-Izvestiya, Volume 16, Number 3
G G Kasparov 1981 Math. USSR Izv. 16 513
https://iopscience.iop.org/article/10.1070/IM1981v016n03ABEH001320
The original Russian version is Izv. Akad. Nauk SSSR Ser. Mat., 1980, Volume 44, Issue 3, Pages 571–636 http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=im&paperid=1739&option_lang=eng