This thesis describes the latest results of the on-going efforts to measure the properties of antihydrogen within the ALPHA collaboration. More specifically, it covers the construction and commissioning of the ALPHA-g experiment , and the plans to measure how antimatter behaves in Earth’s gravitational field. A special emphasis is on the ALPHA-g magnet system used to confine and manipulate the antihydrogen atoms. Tests of methods for calculating magnetic fields relevant for simulations  are covered as well. Amongst the described results from the ALPHA-2 experiment is the characterisation of the fine structure of antihydrogen . The combined result of the measured 1S–2P1/2 and 1S–2P3/2 transitions agrees with the prediction of quantum electrodynamics to 16 parts per billion. The thesis also describes the demonstration of the first laser cooling of antimatter , which paves the way for a measurement of the 1S–2S transition in antihydrogen with hydrogen-like precision, and a measurement of antigravity with 1% precision. Both are future goals of the ALPHA collaboration.