Abstract: After a brief introduction of the Kondo resonance study on quantum dots and using STM on metallic surfaces, two pieces of work will be described: 1) Fano resonance in Anderson impurity systems. It is shown that the broadening of the impurity level leads to an additional and important contribution to the Fano resonance around the Fermi energy, especially in the mixed valence regime. This contribution comes from the interference of the Kondo resonance and the broadened impurity level. The theory can quantitatively explain the STM data not only for systems like Co on Au/Ag/Cu surfaces, but also for Ti on Au/Ag surfaces. (Ref. cond-mat/0311533). 2) Swapping entangled Kondo resonances in parallel-coupled double quantum dots. It is shown that in the Kondo regime with degenerate dot levels, the bonding and antibonding states of the Kondo resonances can be swapped by changing the interdot exchange integral and/or the asymmetric dot-lead coupling ratio. In principle, this process can be used to realize an XOR gate for the quantum computation. (Ref. cond-mat/0403629).