AEgIS (Antimatter experiment: gravity, interferometry, spectroscopy) is an experiment approved by CERN with the goal of studying antihydrogen physics. In AEgIS, antihydrogen will be produced by charge exchange reactions of cold antiprotons with positronium atoms excited in a Rydberg state (n > 20). In the first phase of the experiment, controlled acceleration by an electric field gradient (Stark effect) and subsequent measurement of free fall in a Moire deflectometer will allow a test of the weak equivalence principle. In a second phase, the antihydrogen will be slowed, confined, and laser-cooled to perform CPT studies and detailed spectroscopy. In the present work, after a general description of the experiment, the present status of advancement will be reviewed, with special attention to the production and excitation of positronium atoms.