This encyclopedic, detailed exposition spans all the steps of one-period allocation from the foundations to the most advanced developments. Multivariate estimation methods are analyzed in depth, including non-parametric, maximum-likelihood under non-normal hypotheses, shrinkage, robust, and very general Bayesian techniques. Evaluation methods such as stochastic dominance, expected utility, value at risk, and coherent measures are thoroughly discussed in a unified setting and applied in a variety of contexts, including prospect theory, total return, and benchmark allocation. Portfolio optimization is presented with emphasis on estimation risk, which is tackled by means of Bayesian, resampling, and robust optimization techniques. All the statistical and mathematical tools, such as copulas, location-dispersion ellipsoids, matrix-variate distributions, and cone programming, are introduced.