I was searching stuff related to M.Kac's famous question "Can one hear the shape of the drum ?" I further found results due to Gordon, Webb and Wolpert in the 2D case using Sunada method. Are there any books on this topic explaining the above mentioned stuff and the recent advances? Thanks.
I do not think there is a book entirely dedicated to the isospectrality problem. However, take a look at this survey and references given there.
Check Chapter 3 of "Old and new aspects in spectral geometry" by Craioveanu, Puta and Rassias.