Superconductivity is a phenomenon of zero electrical resistance which occurs when a certain material is cooled below a critical temperature. Since it was first experimentally observed (1911) up to this day, superconductivity has been a subject of research due to the vast potential technological applications. In this thesis, we will study some magnetic properties of YBa_2Cu_3O_6+x monocrystal which play a significant role in superconductivity and the potential technological application. The work is divided into two major parts. The first part, the introductory and theoretical sections, the short summary of the historical development of superconducting materials will be given, along with the current state and the basic theoretical assumptions which explain the phenomenon of superconductivity, which are important for understanding the given experimental data. The theoretical section comprises of three sections in which a short review is given concerning the London model, the physical origin of Cooper pairs and the fundementals of the Ginzburg-Landau theory. In the second part, the experimental data will be presented and analyzed. In the fourth section we will describe the synthesis method of the YBCO monocrystal as well as its structure. Fifth section deals with the magnetic properties of the high temperature superconductors in the context of the YBCO monocrystal. The sixth section describes the experimental methods and results.