  These lecture notes are based on a six-hour series of lectures given at the
XVII Modave summer school in mathematical physics, aimed at Ph.D. students in
high-energy theoretical physics.
  The manuscript starts by briefly stating Goldstone's theorem and emphasises
the motivations behind Goldstone physics; the main asset being the universality
of spontaneous symmetry breaking (SSB) which is the fundamental hypothesis of
Goldstone's theorem. Once the different notions of SSB will be
clarified/reviewed, Goldstone's theorem will be stated and proved. A prediction
of this theorem is the existence of gapless particles, called Nambu-Goldstone
modes (NG modes). From the discussion on Goldstone's results, some aspects of
the NG modes will emerge. Besides to be gapless, they are systematically weakly
coupled at low energy. Therefore, an effective field theory (EFT) building tool
called ``coset construction'' will be presented to explicitly display these
specific features of the NG modes. The coset construction suits our goal since
it is mainly based on the symmetry realisation of the perturbed theory around
the background inducing SSB. From the general obtained EFT, a counting rule for
the NG modes will be derived. The limitations of this rule as well as the still
ongoing generalisation will be discussed (e.g. spacetime symmetry breaking).
The tools developed during this course will be illustrated with a concrete
example in physics: ferromagnetism. The notes end with a brief state of the art
of Goldstone physics. This provides some directions into which the interested
reader could investigate to expand his knowledge on the subject.
  N.B.: No prerequisites are required beside the standard courses of a Master
in theoretical physics.
