The present invention mainly relates to a polymer for delivery of biologically active materials, a complex and a method of synthesis thereof. The polymer comprises a poly(ethylene imine) and at least one monomer, each monomer comprising a modified sugar moiety, preferably galactose, comprising a sulphur atom or a nitrogen atom and a chemical moiety comprising a terminal epoxide for linking the polyethylene imine to the monomer, wherein the sulphur atom or the nitrogen atom links the modified sugar moiety to the chemical moiety. The biologically active material is preferably a gene, siRNA, mRNA or plasmid DNA. Further disclosed is the medical use of said complex in treating a disease caused by a genetic disorder, for example cancer.