This master’s thesis in mathematics aims to make an introduction to the subject of Private Information Retrieval (PIR) by introducing the main ideas of PIR as well as introducing a couple of promising PIR schemes which rates are compared with capacity achieving schemes. The PIR viewpoint taking in this thesis is that of information theoretic privacy. The thesis presents coded distributed storage systems and how these should be considered in the PIR context. One of the primary tools in the PIR schemes of this thesis is Generalised Reed-Solomon (GRS) codes. It is shown that these have very compelling properties in the PIR setup. A considerable amount of server-side computation must be carried out in the presented schemes. Hence, this thesis presents a scheme variant of one of the schemes that uses subfield subcodes of GRS codes (alternant codes) which reduces the computational complexity of the server response computation. Considerations towards a subfield subcode version of the second scheme are also presented