  The well-quasi-orders (WQO) play an important role in various fields such as
Computer Science, Logic or Graph Theory. Since the class of WQOs lacks closure
under some important operations, the proof that a certain quasi-order is WQO
consists often of proving it enjoys a stronger and more complicated property,
namely that of being a better-quasi-order (BQO).
  Several articles contains valuable introductory material to the theory of
BQOs. However, a textbook entitled "Introduction to better-quasi-order theory"
is yet to be written. Here is an attempt to give a motivated and self-contained
introduction to the deep concept defined by Nash-Williams that we would expect
to find in such a textbook.
