This thesis details the development and commissioning of the ALPHA antihydrogen trapping apparatus. It discusses the history of antimatter physics that led to and enabled the design of the apparatus. It discusses the importance of antihydrogen trapping in testing one of the basic assumptions of the Standard Model of particle physics (that of CPT invariance). It goes on to discuss the design and construction of the apparatus. Finally, it presents results that demonstrate antihydrogen formation in the new magnetic field configurations that together constitute a magnetic minimum trap for neutral antihydrogen. This is an important preliminary result for any antihydrogen trapping apparatus, and confirms that the ALPHA apparatus does present a potential route towards laser spectroscopy of antihydrogen.