  Kadath is a library that implements spectral methods in a very modular
manner. It is designed to solve a wide class of problems that arise in the
context of theoretical physics. Several types of coordinates are implemented
and additional geometries can be easily encoded. Partial differential equations
of various types are discretized by means of spectral methods. The resulting
system is solved using a Newton-Raphson iteration. Doing so, Kadath is able to
deal with strongly non-linear situations. The algorithms are validated by
applying the library to four different problems of contemporary physics, in the
fields of gauge field theory and general relativity
