Chapter 3 derives the gap equation and determines the critical transition temperature as well as the zero-temperature energy gap as a function of coupling constant for d-wave superconductors. The energy dependence of the density of states and its effects on the temperature dependence of the gap function, entropy and other thermodynamic quantities are also discussed. Low energy nodal excitations lead to characteristic power-law behaviors in the specific heat or other thermodynamic response functions of d-wave superconductors at low temperatures, in contrast to the activated behaviors in s-wave superconductors. The probability density current and charge density current operators of d-wave quasiparticles, together with the gap operators in the continuum limit, are derived and discussed with the BdG framework.