Abstract: Self-similar processes are stochastic processes that are invariant in distribution under a suitable time scaling. These processes are often used as models for various random phenomena. The most known self-similar process is the fractional Brownian motion (fBm), which can be defined as the only Gaussian self-similar process with stationary increments. Its stochastic analysis constitutes an important research direction in probability theory nowadays. The Hermite processes are non-Gaussian extensions of the fBm. These processes, which are are also self-similar, with stationary increments and exhibit long-range dependence, have been also intensively studied in the last decades. The purpose of these lectures is to present the basic properties of the Hermite processes and to discuss some elements of the stochastic analysis with respect to them.