Permutation is a way of arranging all the elements of a given set into a sequence or an order. Random permutations are commonly used in different areas of mathematics and computer science, such as combinatorics and artificial intelligence, as well as in the everyday life; for arranging decks of cards, music play-lists, etc. The aim of this master’s thesis was to describe and analyze algorithms for generating random permutations, also known as shuffling algorithms. The first part of the thesis focused on defining shuffling algorithms and describing techniques later utilized for comparing their complexities. We also presented examples of how-not-to-shuffle, showing algorithms that are either biased or nonoptimal thus should not be used in data shuffling. The second part enumerated shuffling algorithms by identifying their steps, calculating complexities and displaying their step-by-step execution on a given example set. Among others, we mentioned the Fisher–Yates shuffle, one of the most widely recognized algorithms in computer science. Furthermore, we addressed frequent causes of bias in shuffling algorithms, simultaneously providing their solutions. Finally, the thesis validates given algorithms by implementing them in the programming language C# and executing the code with substantial input data. The outcomes are presented and compared, resulting in a conclusion that the modern, in-place version of the Fisher–Yates shuffle is both fast and applicable on arbitrarily large data sets.