This thesis deals with random walks on a symmetric group, namely the models that are used to describe the shuffling of a deck of cards. In this work we focus on the question of mixing speed (the speed of convergence of the marginal distribution of a random walk to its stationary distribution). We ask ourselves a basic question when shuffling cards: how many times do the cards need to be shuffled so that they are already sufficiently randomly distributed. The random walk model, which is a Markov chain, is the mathematical formalization of the card shuffling process. We transfer the card shuffling problem to the problem of estimating the distance between the marginal distribution of this Markov chain and its stationary distribution. We then u...