The aim of this work is to study lattice structures made by additive manufacturing technology, made with SLM process in particular. Starting from a metal powder and thanks to a laser source, a specific part is produced layer by layer. This kind of technology allows the production of objects with complex shapes that would not be possible using traditional manufacturing methods. This work is divided into 5 chapters. The first chapter, "Introduction", provides a quick overview of additive technology and its advantages. It also introduces the concept of lattice structures with definitions and a first classification. The second chapter, "State of Art", illustrates some theoretical concepts that are present today in the literature on the subject of cellular material.