ULySS: A Full Spectrum Fitting Package. Aims. We provide an easy-to-use full-spectrum fitting package and explore its applications to (i) the determination of the stellar atmospheric parameters and (ii) the study of the history of stellar populations. Methods. We developed ULySS, a package to fit spectroscopic observations against a linear combination of non-linear model components convolved with a parametric line-of-sight velocity distribution. The minimization can be either local or global, and determines all the parameters in a single fit. We use chi2 maps, convergence maps and Monte-Carlo simulations to study the degeneracies, local minima and to estimate the errors. Results. We show the importance of determining the shape of the continuum simultaneously to the other parameters by including a multiplicative polynomial in the model (without prior pseudo-continuum determination, or rectification of the spectrum). We also stress the benefice of using an accurate line-spread function, depending on the wavelength, so that the line-shape of the models properly match the observation. For simple models, i. e., to measure the atmospheric parameters or the age/metallicity of a single-age stellar population, there is often a unique minimum, or when local minima exist they can unambiguously be recognized. For more complex models, Monte-Carlo simulations are required to assess the validity of the solution. Conclusions. The ULySS package is public, simple to use and flexible. The full spectrum fitting makes optimal usage of the signal.