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The last decades have proved fruitful for astronomy, astrophysics and cosmology from an observational point of view. The exciting late-time acceleration observation has utterly changed the perspectives of theoretical cosmologists, while the direct detection of gravitational waves emerging from the neutron star and other astrophysical binary objects merging, has also established a new scientific discipline, the gravitational wave astronomy. Apart from these striking observations, inflation in its various aspects and cosmological bounces are severely constrained by the Planck data, while other problems in both astrophysics and cosmology seem to emerge, thickening significantly the plot in astrophysics and cosmology, like the Ho tension problem and the probability to have neutron stars with equal or larger masses that two solar masses. Topping that, the LISA mission in about a decade from now, is expected to further enlighten the physics of the early Universe, since it will offer the possibility of detecting stochastic gravitational-wave modes of inflation that re-entered the Hubble horizon quite early near the end of inflation, during the mysterious reheating and radiation domination era. To this end, in this purely 4-day online conference, we aim to bring leading experts in the fields of cosmology and astrophysics, to discuss and present their perspectives in their field of expertise, and discuss all the possible solutions to the present and future problems that might seem to emerge. We hope with this online event, due to the COVID19 pandemic, to constructively stimulate scientifically the participants to discover the works of others realtime and to exchange knowledge. At the end of the conference, a round table discussion will take place with topics of current cosmological and astrophysical interest.