We consider here estimation of an unknown probability density $s$ belonging to $\Bbb{L}_2(\mu)$ where $\mu$ is a probability measure. We have at hand $n$ i.i.d.\ observations with density $s$ and use the squared $\Bbb{L}_2$-norm as our loss function. The purpose of this paper is to provide an abstract but completely general method for estimating $s$ by model selection, allowing to handle arbitrary families of finite-dimensional (possibly non-linear) models and any $s\in\Bbb{L}_2(\mu)$. We shall, in particular, consider the cases of unbounded densities and bounded densities with unknown $\Bbb{L}_\infty$-norm and investigate how the $\Bbb{L}_\infty$-norm of $s$ may influence the risk. We shall also provide applications to adaptive estimation and aggregation of preliminary estimators. Although of a purely theoretical nature, our method leads to results that cannot presently be reached by more concrete ones.