I present a motivation of several areas where the Multigrid techniques can be employed. I present typical areas where the multigrid solver might be employed. I give an introduction to smoothers and how one might choose a preconditionor as well as an introduction of the Multigrid technique used. Then I do a study of the Multigrid technique while adjusting the environment conditions of the solver and the problem such as anisotropies, the grid-levels used, the preconditionor smoothing steps, the coordinate system and the start vector. The problem solved here was a simple Poisson problem. The Multigrid program used an F-cycle in this paper. I include performance study sections displaying results of the solver behavior under the different conditions.