It has been known that Fourier transformation is a very useful tool since it transform a variable from its form $x$ to a correlated basis.
However, is there any other decomposition or transformation method that can transform variables and functions into other basis, and what's their advantage and disadvantage compared to Fourier transformation? (for example, it seems to me that Laplace transformation can be used to solve partial differential equations, but why it is so rarely used in daily occasions?)