the latter to the studies of a simplest (isotropic) models of an early Universe have shown that the quantum nature of the geometry qualitatively modifies the global picture of its evolution. Namely, the big bang singularity is dynamically resolved as it is replaced by a so called big bounce [@aps-prl] which connects the current (expanding) Universe with a contracting one preceding it. The results initially obtained numerically for the flat isotropic model with massless scalar field [@aps-det; @aps-imp] were shown to be general features of that model [@acs; @cs] and next extended to more general matter fields [@negL; @posL; @infl] and topologies [@spher; @hiperb] as well as to less symmetric systems: anisotropic [@boj-b1; @chiou-b1; @szulc-b1; @b1-mmp; @b1-evo; @awe; @b2] and some classes of the inhomogeneous ones [@gowdy]. Also, although the theory originates from the canonical framework, a connection with the *spin foam* [@sf] models was made through the studies of the path integral in LQC [@ah] as well as the analysis of the cosmological models within the spin foam models themselves [@rv]. Another avenue of extensions is the perturbation theory around the cosmological solutions [@pert]. The elements of its mathematical structure of LQC, which was initially formulated in [@abl], were 