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This book describes the first ever antimatter free-fall experiment, known as ALPHA-g, which measures the effect of Earth's gravity on antimatter atoms. The effect of gravity on antimatter has been a subject of speculation for decades and experimental measurements have been a long-term goal of the field. The experiment found that it does indeed fall down, and this represents a first step toward precise measurements of gravity on antimatter. Any observed difference, no matter how small, would have a profound impact on physics. This book presents major contributions to the ALPHA-g experiment. In particular, the author developed precise magnetic field measurement techniques and led an extensive campaign to characterize magnetic fields in the ALPHA-g experiment, a key enabling factor without which the experiments would not have been possible. The author was also one of the leaders of an effort to design and install new antimatter traps in the apparatus that will be required for future measurements. The book shows the big picture of the work in the context of the wider field, and gives clear and concise descriptions of the experimental protocol, the required supporting measurements, and hardware developments needed for this measurement and for those in the future.