π1π_1 of smooth points of a log del Pezzo surface is finite : I

A log del Pezzo surface is a normal projective surface $S$ defined over the field of complex numbers, such that $S$ has at most quotient singularities and $-K_S$ is ample, where $K_S$ denotes the canonical divisor. The main result of this work is the following theorem: \proclaimit{Theorem.}{Let $S$ be a log del Pezzo surface. Then the fundamental group of the space of smooth points of $S$ is finite.} We also give a quite precise description of the singularities of $S$ when $S$ has Picard group of rank 1