Information-theoretic tools are used to derive minimax risk bounds for density estimation. A metric entropy condition alone determines the minimax rate of convergence in each class of density functions. To achieve the minimax rates simultaneously for multiple function classes, we consider lists of finite-dimensional approximating models and use model selection criteria to select adaptively a good model based on data. The use of many candidate models, as in the case of subset selection, provides more flexibility for adaptation, yet significant selection bias can occur with criteria such as AIC. We incorporate a model complexity term in the model selection criteria to handle this selection bias. It is shown that the risk of the estimated density is bounded by an index of resolvability, which characterizes the best tradeoff among approximation error, estimation error, and model complexity. As an application, we show that the optimal rate of convergence is simultaneously achieved for density in the Sobolev space W_2^s(U) without knowing the smoothness parameter s and norm parameter U in advance.