Additive manufacturing (AM) of polymers and metals is already established in the industry. Materials such as glass create significant challenges based on their material properties. Especially mechanical and thermal properties as well as the viscosity behavior are difficult to handle. So far, only few specialized glass AM processes exist and are established in research and development. The Laser Glass Deposition (LGD) process offers the possibility to deposit glass fibers without using binder materials. For the application area of optical components, manufactured parts must fulfill high requirements for transparency, surface quality, material purity and homogeneity of the material. Investigations on the printing of individual single-layer quartz glass structures have already been carried out with the LGD process. Within this article the influence of laser power, axis speed and fiber feeding speed on the deposition characteristics is investigated shortly. Subsequently, a multilayer deposition is investigated to manufacture solids with an optical transparency.