Self-tuning of the cosmological constant

Here, I discuss the cosmological constant problems, in particular paying attention to the vanishing cosmological constant. There are three cosmological constant problems in particle physics. Hawking's idea of calculating the probability amplitude for our Universe is peaked at (Lambda) over bar = 0 which I try to obtain after the initial inflationary period using a self-tuning model. I review what has been discussed on the Hawking type calculation with H-2 Lagrangian, and present a (probably) correct way to calculate the amplitude, and show that the Kim-Kyae-Lee self-tuning model allows a finite range of parameters for the (Lambda) over bar = 0 to have a singularly large probability, approached from the AdS side.