In this thesis we mainly focus on the helicodal surface with light-like axis in Minkowski ?- space. This thesis, including six section, the first and second section is dedicated to the introduction of other chapter. We denote by E?? the ? dimensional Minkowski Space with Lorentz metric g(x,y)=-x ?y ? #??; x ?y ? #??; x ? y ?. A vector V of E?? is said to be timelike if?V,V?? ? , spacelike if ?V,V?? ? or V=? and lightlike or null if ?V,V? = ? . A helicoidal motion around the axis w can be defined as a transformation of E?? defined: gv: x ? g v(x)= A(v)x T #??; (hv)w, x = (x?, x?, x?)? E?? , v ? R, where h is a non-zero constant We defined the third fundamental form ? of M, if the third fundamental form ? is non-degenerate , then it can be regared as a (psuedo) Riemannian metric and the Laplacian ?? with respect to ? can be defined formally on the (pseudo) Riemannian manifold M. By a Lorentz rotation around an axis , we mean the ?-parameter group of Lorentzian transformations leaving the axis pointwise fixed. Let ?: (a,b) ? II be a plan curve in E?? and ? a straight line in ? wich does not intersect curve .