The aim of this work is to address the problem of White Matter Lesion (WML) segmentation employing Magnetic Resonance Imaging (MRI) images from Multiple Sclerosis (MS) patients through the application of deep learning. A U-net based architecture containing a contrastive path and an expanding path prior to the final pixel-wise classification is implemented. The data are provided by the Ippokratio Radiology Center of Ioannina and include Fluid-Attenuated Inversion Recovery (FLAIR) MRI images from 30 patients in three phases, baseline and two follow ups. The prediction results are quite significant in terms of pixel-wise classification. The implemented deep learning model demonstrates Dice coefficient 0.7292, Precision 75.92% and Recall 70.16% in 2D slices of FLAIR MRI non-skull stripped images.