  In these notes we review the S-matrix theory in (1+1)-dimensional integrable
models, focusing mainly on the relativistic case. Once the main definitions and
physical properties are introduced, we discuss the factorization of scattering
processes due to integrability. We then focus on the analytic properties of the
two-particle scattering amplitude and illustrate the derivation of the
S-matrices for all the possible bound states using the so-called bootstrap
principle. General algebraic structures underlying the S-matrix theory and its
relation with the form factors axioms are briefly mentioned. Finally, we
discuss the S-matrices of sine-Gordon and SU(2), SU(3) chiral Gross-Neveu
models. This is part of a collection of lecture notes for the Young Researchers
Integrability School, organized by the GATIS network at Durham University on
6-10 July 2015.
