Isolation or in vitro assembly of the Cas9-crRNA complex of the Streptococcus thermophilus CRISPR3/Cas system and use for cleavage of DNA bearing a nucleotide sequence complementary to the crRNA and a proto-spacer adjacent motif. Methods for site-specific modification of a target DNA molecule using an RNA-guided DNA endonuclease comprising at least one RNA sequence and at least one of an RuvC active site motif and an HNH active site motif; for conversion of Cas9 polypeptide into a nickase cleaving one strand of double-stranded DNA by inactivating one of the active sites (RuvC or HNH) in the polypeptide by at least one point mutation; for assembly of active polypeptide-polyribonucleotides complex in vivo or in vitro; and for re-programming a Cas9-crRNA complex specificity in vitro or using a cassette containing a single repeat-spacer-repeat unit.