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The covariant density functional theory (CDFT) with a few number of parameters allows a very successful description of the properties of nuclei all over the nuclear chart. The recent progress on the application of the CDFT as well as its extensions for a series of interesting and hot topics in nuclear structure and nuclear astrophysics are summarized. In particular, the newly proposed point-coupling parametrization PC-PK1 and the application of the CDFT to the single particle level of the radioactive neutron-rich doubly magic nucleus 132Sn, the deformed halo in nuclei, and the β decay life-time of neutron rich nuclei are discussed in details

Covariant density functional theory and applications in nuclear physics and r-process