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Due to the complexity of the material structures, the experimental results for high Tc cuprates, including YBa₂Cu₃O₇ (YBCO), are far more difficult to understand than those for conventional low Tc superconductors of simple structures. It is our view that many experimental results cannot be understood without careful first-principles calculations to include realistic electronic structures and electron-phonon (e-ph) interaction effect in these materials. We present the results of first-principles calculations for the electronic structure, e-ph interaction, and the temperature dependence of the anisotropic superconducting gap in YBCO. Our calculations show that the smaller gaps at some k-points on the Fermi surface of YBCO collapse earlier than the larger ones as the temperature increases, that leads to gapless state on the Fermi surface of YBCO even below Tc. The work was funded in part by NSF (Award # HRD 1736136 ) and ARO (Award # W911NF-15-1-0483).