In this work, we were the first to show the possibility of synthesizing polydimethylsiloxanes (PDMSs) with azidopropyl-functional groups at the silicon atom by the classical methods for PDMS synthesis, that is, ring-opening polymerization (ROP) and catalytic rearrangement of siloxanes in the presence of a strong acid (CF3SO3H). The suggested method was used to obtain PDMSs containing azidopropyl-functional groups at both ends of the polymer chain (telechelics) as well as PDMSs with irregular structures containing different fractions (5-50%) of azidopropyl-functional groups in the main polymer chain. The suggested method also proved to be efficient for synthesizing PDMSs containing both azidopropyl- and hydridosilyl-functional groups simultaneously. As a result, PDMSs with different mutual arrangements of two types of functional groups along the PDMS chain were obtained. The method for the catalytic rearrangement of low-molecular-weight siloxanes that we used made it possible to obtain azidopropyl-functional PDMSs in a wide range of molecular weights from 2000 to 88,000 according to gel permeation chromatography (GPC) data. The possibility of further modification of the resulting azidopropyl-functional PDMS, as well as multifunctional PDMSs containing azidopropyl- and hydridosilyl-functional groups simultaneously, by azide-alkyne cycloaddition reactions was demonstrated. The polymers obtained were characterized by H-1 and Si-29 NMR spectroscopy and by GPC.