In the previous lecture we have introduce and discussed the concept of affinely-rigid, i.e., homogeneously deformable body. Some symmetry problems and possible applications were discussed. We referred also to our motivation by Euler ideas. Below we describe the general principles of the quantization of this theory in the Schrödinger language. The special stress is laid on highly-symmetric, in particular affinely-invariant, models and the Peter-Weyl analysis of wave functions.