  These notes give an introduction to the equivalence problem of sub-Riemannian
manifolds. We first introduce preliminaries in terms of connections, frame
bundles and sub-Riemannian geometry. Then we arrive to the main aim of these
notes, which is to give the description of the canonical grading and connection
existing on sub-Riemann manifolds with constant symbol. These structures are
exactly what is needed in order to determine if two manifolds are isometric. We
give three concrete examples, which are Engel (2,3,4)-manifolds, contact
manifolds and Cartan (2,3,5)-manifolds.
  These notes are an edited version of a lecture series given at the
\href{https://conference.math.muni.cz/srni/}{42nd Winter school: Geometry and
Physics}, Snr\'i, Check Republic, mostly based on other earlier work. However,
the work on Engel (2,3,4)-manifolds is original research, and illustrate the
important special case were our model has the minimal set of isometries.
