The relation of quarteting and clustering in atomic nuclei is discussed based on symmetry-considerations. This connection enables us to predict a complete high-energy cluster spectrum from the description of the low-energy quartet part. As an example
the $^{28}$Si nucleus is considered, including its well-established ground-state region, the recently proposed superdeformed band, and the high-lying molecular resonances.
Algebraic models are proposed for the description of the shell-like quarteting of the nucleons both on the phenomenologic and on the semimicroscopic levels. In the previous one the quartet is considered as a structureless object, while in the latter
one its constituents are treated explicitely. The excitation spectrum is generated by the SU(3) formalism in both cases. An application to the $^{20}$Ne nucleus is presented.
We discuss the role of the broken symmetries in the connection of the shell, collective and cluster models. The cluster-shell competition is described in terms of cold quantum phases. Stable quasi-dynamical U(3) symmetry is found for specific large deformations for a Nilsson-type Hamiltonian.
The relation of the shell, collective and cluster models of the atomic nuclei is discussed from the viewpoint of symmetries. In the fifties the U(3) symmetry was found as their common part for a single shell problem. For multi major-shell excitations
, considered here, the U(3)$otimes$U(3) dynamical symmetry turns out to be their intersection.
