Volume one of The Full-Stack AI Engineering Series, covering the infrastructure layer of a production large language model platform. Twelve chapters develop NexusCore, a fictional routing and observability gateway operated by a fictional regulated fintech called Nebula Financial, and treat inference and serving foundations, multi-cloud and hybrid topology, learned routing policies expressed as versioned artifacts, edge and on-device escalation, speculative decoding as a latency primitive, distributed and pipelined inference, observability, router lifecycle security, and compliance as evidence the system produces by design. A case study reconstructs a trading-desk outage and the router rollback that followed, and a closing chapter assembles the full reference architecture. Specifications throughout are conceptual, presenting schemas, policy objects, trace shapes and architecture diagrams rather than production code. Addressed to site reliability engineers, cloud architects and platform engineers who have been given responsibility for AI workloads.