  In this paper, we give a fully detailed exposition of computing fundamental
groups of complements of line arrangements using the Moishezon-Teicher
technique for computing the braid monodromy of a curve and the Van-Kampen
theorem which induces a presentation of the fundamental group of the complement
from the braid monodromy of the curve.
  For example, we treated the cases where the arrangement has t multiple
intersection points and the rest are simple intersection points. In this case,
the fundamental group of the complement is a direct sum of infinite cyclic
groups and t free groups. Hence, the fundamental groups in these cases is
``big''. These calculations will be useful in computing the fundamental group
of Hirzebruch covering surfaces.
