  The usage of elementary submodels is a simple but powerful method to prove
theorems, or to simplify proofs in infinite combinatorics. First we introduce
all the necessary concepts of logic, then we prove classical theorems using
elementary submodels. We also present a new proof of Nash-Williams's theorem on
cycle-decomposition of graphs, and finally we improve a decomposition theorem
of Laviolette concerning bond-faithful decompositions of graphs.
