  This paper is an attempt to present and discuss at some length the Singular
Manifold Method. This Method is based upon the Painlev\'e Property
systematically used as a tool for obtaining clear cut answers to almost all the
questions related with Nonlinear Partial Differential Equations: Lax pairs,
Miura, B\"acklund or Darboux Transformations as well as $\tau$-functions, in a
unified way. Besides to present the basics of the Method we exemplify this
approach by applying it to four equations in $(1+1)$-dimensions. Two of them
are related with the other two through Miura transformations that are also
derived by using the Singular Manifold Method.
