  The aim of this survey paper is to present a complete direct proof of the
well celebrated cornerstone result in Loewner Theory, originally due to Kufarev
et al [Trudy Tomsk. Gos. Univ. Ser. Meh.-Mat. 200 (1968) 142-164. MR0257336 (41
#1987)], stating that the family of the hydrodynamically normalized conformal
self-maps of the upper-half plane onto the complement of a gradually erased
slit satisfies, under a suitable parametrization, the chordal Loewner
differential equation. The proof is based solely on basic theorems of Geometric
Function Theory combined with some elementary topological facts and does not
require any advanced technique.
