Graphene is a single atomic layer 2D graphite that has unusual properties that would open up wide industrial applications. As graphite is the toughest material on earth, challenges exist to cut and shape the materials. This MPhil thesis presents the outcome of femtosecond laser micro-patterning of single layer graphene on a glass substrate, which has resulted in a journal publication. A literature review was carried out to understand the process, basic characteristics and challenges in laser micro/nano fabrication, and the physical properties of glass and graphene.Femtosecond laser surface patterning of glass was carried out as a preliminary study for the preparation of laser patterning on graphene. A simple method to determine the focal point of laser beam was studied. With this method, the focal point of laser beam could be precisely controlled onto the glass surface and the smallest micro patterns could be induced. Craters with diameters down to 2 µm (including the ring-bumps around) were demonstrated on glass surface. The damage threshold of the glass was determined to be about 3.0 J/cm2, and this value will be useful for future study of laser processing of graphene.The main part of the research was on femtosecond laser patterning and profile cutting of graphene on a glass substrate. The cutting of graphene was achieved in air and argon. By translating the graphene sample with respect to the laser beam, continuous micro-channels were carved. The cutting geometry can be controlled by varying the laser fluence and the scanning path. In addition, 1~2 μm wide graphene micro-ribbons were hatched out. The ablation threshold of graphene was determined to be 0.16~0.21 J/cm2. With the laser fluence higher than the ablation threshold, graphene was ablated rapidly and removed completely without damaging the glass substrate. Atomic force microscopy (AFM) and Raman spectroscopy have been used to confirm the ablation of graphene. Time domain finite difference modelling was employed to understand the thermal history of the laser ablation process.