This chapter introduces the foundational elements of scattering amplitudes.
It is meant to be accessible to readers with only a basic understanding of
quantum field theory. Topics covered include: the four-dimensional
spinor-helicity formalism and the colour decomposition of Yang-Mills scattering
amplitudes; the study of soft and collinear limits of Yang-Mills and gravity
amplitudes; the BCFW recursion relation and generalised unitarity, also in the
superamplitudes formalism of $\mathcal{N}{=}4$ supersymmetric Yang-Mills; an
overview of standard and hidden symmetries of the $S$-matrix of
$\mathcal{N}{=}4$ supersymmetric Yang-Mills, such as the conformal, dual
conformal and Yangian symmetries; and a brief excursus on form factors of
protected and non-protected operators in Yang-Mills theory. Several examples
and explicit calculations are also provided.
