  These notes give an introduction to the Strominger system of partial
differential equations, and are based on lectures given in September 2015 at
the GEOQUANT School, held at the Institute of Mathematical Sciences (ICMAT) in
Madrid. We describe the links with the theory of balanced metrics in hermitian
geometry, the Hermite-Yang-Mills equations, and its origins in physics, that we
illustrate with many examples. We also cover some recent developments in the
moduli problem and the interrelation of the Strominger system with generalized
geometry, via the cohomological notion of string class.
