  Lipschitz equivalence of self-similar sets is an important area in the study
of fractal geometry. It is known that two dust-like self-similar sets with the
same contraction ratios are always Lipschitz equivalent. However, when
self-similar sets have touching structures the problem of Lipschitz equivalence
becomes much more challenging and intriguing at the same time. So far the only
known results only cover self-similar sets in $\bR$ with no more than 3
branches. In this study we establish results for the Lipschitz equivalence of
self-similar sets with touching structures in $\bR$ with arbitrarily many
branches. Key to our study is the introduction of a geometric condition for
self-similar sets called {\em substitutable}.
