The Apollo Project was the first flight system to deploy with a digital, general-purpose computer made of integrated circuits at its core: the Apollo Guidance Computer (AGC). It was a complete research project: no IC computer had run consecutively for more than a few hours, sophisticated programming techniques were unknown and the interactive human/computer interface had to be invented and made to appeal to astronauts opposed to machine interference in flight operations. In this talk I'll give the historical context for the AGC, discuss its initial design and the evolution of this design as the Apollo Project progressed. We'll do a deep-dive on the machine architecture and note how tight integration with a special-purpose vehicle admitted incredibly sophisticated behaviour from a primitive machine. We'll further discuss the human/computer interface for the AGC, how the astronaut's flight roles dictated the computer's role and vice versa. Motivating examples from select Apollo flights will be used. Throughout, we'll keep an eye on lessons to be gleaned from the experience of engineering the AGC and how we can adapt these lessons to modern computer systems in mission-critical deployments.