This thesis addresses the “2D Irregular Packing problem”, a combinatorial optimization challenge with significant applications in industries such as manufacturing, furniture production, textiles and aerospace. The problem focuses on efficiently arranging two-dimensional objects of irregular shapes on a surface with the goal of minimizing unused space and maximizing material utilization. Given the problem’s NP-complete nature, finding an optimal solution is computationally infeasible for most real-world scenarios. As a result, in literature approximate solutions are typically sought using heuristic and metaheuristic algorithms. This thesis first addresses the nesting problem through the algorithms present in the literature. The geometric problem of positioning a polygon into a hole or relative to another polygon is treated with two methods: the Envelope Polygon and the No-Fit Polygon.