This thesis aims to introduce the reader to the mathematical principles underlying X-ray computed tomography. It begins with the derivation of both filtered and unfiltered back-projection reconstruction techniques. Following this, the thesis delves into two algorithms based on algebraic reconstruction techniques (ART): the Simultaneous Algebraic Reconstruction Technique (SART) and the Discrete Algebraic Reconstruction Technique (DART). This includes the derivation and implementation of both methods and the analysis and comparison of theDART algorithmto the aforementioned methods, all using simulated data. These ART methods approach the reconstruction problem by iteratively optimizing a large system of linear equations. In addition, DART leverages prior knowledge on grey values to steer the final reconstruction towards one that only contains these pre-determined grey values. Based on the experiments using simulated data it is shown that DART effectively deals with both errors in the approximation of the grey values as well as with noisy projection data. Furthermore, it is found that DART computes relatively accurate reconstructions using only a small number of projections or projections from a small angular range.