General introduction to cosmology of modified gravity is given. It is shown that different forms of modified gravity are possible: many of them being consistent with Solar system tests and cosmological bounds. Special attention is paid to F(R) gravity. It is shown that such theory may naturally describe the early-time inflation with late-time acceleration(dark energy epoch). Realistic versions of F(R) gravity are proposed. The inflationary indices are shown to be consistent with Planck experiment. New ghost- free versions of modified gravity are introduced and their cosmological evolution is studied. It is shown that it may naturally give the unification of inflation with dark energy while scalar field which appears there plays the role of dark matter.

Prof. Sergei D. Odintsov is ICREA Research Professor at ICE (CSIC-IEEC) Barcelona since 2003. He wrote about 600 journal articles, with about 40000 citations. Three ms written while in ICREA and two books were cited more than 1000 times. Foreign Member of the Royal Norwegian Academy, member of European Phys. Soc. and Italian Grav. Soc. Awarded by Amaldi Gold Medal: European Prize for Gravitational Physics 2014. Editorial Board Member of six journals and referee of about 20 journals (with excellence certificates from PLB, EPL, PRD, PRL and EPJC). Hirsh index h=95(Google Scholar), h=80(Web of science) and h=92(inspirehep). Speaker/lecturer of about 120 conf. and Org. Comm.member/ organizer of about 40 int.workshops. Top Cited Thomson-Reuters/Clarivate Analytics Researcher in 2014, 2015, 2016, 2017, 2018. Web.of Science 2017 Award. Silver Medal(2017) and Honorary Professorship (2019) of TSPU, Tomsk. Main achievments: the first modified gravity to unify inflation and dark energy in realistic way (including also radiation/matter dominance and QG effects for inflation). Proposal of new highly-citable models: modified F(G) gravity; F(R,T gravity), generalized holographic dark energy.

Useful link: https://indico-tdli.sjtu.edu.cn/event/96/