Nanochemistry is a science connected with obtaining and studying of physical-chemical properties of particles having sizes on the nanometer scale. This book addresses polymer synthesis which, according to Melikhov's classification, is automatically part of nanochemistry. This is determined as far as polymeric macromolecules (more precisely macromolecular coils) belong to nanoparticles and polymeric sols and gels - to nanosystems. Catalysis on nanoparticles is one of the most important sections of nanochemistry. The majority of catalytic systems are nanosystems. At heterogeneous catalysis the active substance is tried to deposit on carrier in nanoparticles form in order to increase their specific surface. At homogeneous catalysis active substance molecules have often in themselves nanometer sizes. The most favorable conditions for homogeneous catalysis are created when reagent molecules are adsorbed rapidly by nanoparticles and are desorbed slowly but have high surface mobility and, consequently, high reaction rate on the surface and at the reaction molecules of such structure are formed at which desorption rate is increased sharply. If these conditions are realised in nanosystem with larger probability than in macrosystem, then nanocatalyst has the raising activity that was observed for many systems.