The invention provides a novel polyvinyl acetal having N-vinylamide monomer units in the molecule, and provides a binder with the novel polymer for ink or paint and for ceramic forming. Compared with conventional polyvinyl acetals, the novel polymer lowers the solution viscosity and increases the solid content (pigment content) of ink or paint in which the polymer serves as a binder. The binder with the novel polymer for ceramic molding enables production of thin and homogeneous ceramic green sheets of high strength.