The TDHF theory was first proposed by Dirac and its application to nuclear physics started in the 1970s. The readers are intended to refer to other articles in this Research Topic for discussions on experimental as well as other theoretical studies. In section 4, recent advances of theoretical approaches are outlined, along with a discussion on possible future applications. In section 3, the current status of the MNT study with TDHF is given. In section 2, the theoretical framework of TDHF is succinctly recalled. This review briefly digests recent advances of microscopic reaction theories to stimulate new ideas for the future study of MNT reactions. Therefore, the study of MNT reactions is listed as one of the key subjects at the current and future RI beam facilities, such as RIBF (RIKEN, Japan), HIRFL-CSR and HIAF (IMP, China) 1, RAON (RISP, Korea), DRIB (FLNR, Russia) 2, SPIRAL2 (GANIL, France), FAIR (GSI, Germany) 3, SPES (INFN, Italy) 4, FRIB (MSU, USA), and so on. The production of neutron-rich superheavy nuclei in the island is highly desired, as it would provide a new stringent constraint for microscopic theories. Furthermore, the superheavy nuclei produced so far are neutron-deficient ones, and the predicted island of stability has not yet been reached. Needless to say, the historic detection of gravitational waves from a merger of two neutron stars, GW170817, together with radiation from a short γ-ray burst, GRB 170817A, followed by a kilonova makes it a timely and imperative task to unveil inherent properties of the nuclei far away from stability. For instance, besides the fundamental interest in nuclear structures such as shell evolution and shape transitions, properties of extremely neutron-rich nuclei are crucial to fully understanding the detailed scenario of r-process nucleosynthesis. This possibility makes the study of MNT both fascinating and important. Multinucleon transfer (MNT) reactions may be a promising means to produce yet-unknown, neutron-rich unstable nuclei, whose production is difficult by other methods.
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