This is the first of two volumes consisting of lectures given at conferences held in 2019 to celebrate the seventieth birthday of Shing-Tung Yau: at Harvard University (May), at the University of Rome (May/June), at the Chinese University of Hong Kong (June), at the 8th ICCM Congress at Tsinghua University (June), at Lehigh University in Pennsylvania (November), and elsewhere. Included here are: Werner Ballmann on "Bottom of spectra and coverings" Robert J. Berman with "An invitation to Kähler–Einstein metrics and random point processes"; Duong H. Phong on "Unification of the Kähler–Ricci and anomaly flows"; Cumrun Vafa on "SCFTs, holography, and topological strings"; Stephen S.-T. Yau with "Recent results on k -th Yau algebras over simple elliptic singularities"; Kefeng Liu on "Global methods of solving equations on manifolds"; Chuu-Lian Terng on "The geometric airy curve flow"; and Valentino Tosatti on "Collapsing Calabi–Yau manifolds."