The design of an IPTV multicast system for the Internet backbone network is presented and explored through extensive simulations. In the proposed system, a resource reservation algorithm such as RSVP, IntServ, or DiffServ is used to reserve resources (i.e., bandwidth and buffer space) in each router in an IP multicast tree. Each router uses an Input-Queued, Output-Queued, or Crosspoint-Queued switch architecture with unity speedup. A recently proposed Recursive Fair Stochastic Matrix Decomposition algorithm used to compute near-perfect transmission schedules for each IP router. The IPTV traffic is shaped at the sources using Application-Specific Token Bucker Traffic Shapers, to limit the burstiness of incoming network traffic. The IPTV traffic is shaped at the destinations using Application-Specific Playback Queues, to remove residual network jitter and reconstruct the original bursty IPTV video streams at each destination. All IPTV traffic flows are regenerated at the destinations with essentially zero delay jitter and essentially-perfect QoS. The destination nodes deliver the IPTV streams to the ultimate end users using the same IPTV multicast system over a regional Metropolitan Area Network. It is shown that all IPTV traffic is delivered with essentially-perfect end-to-end QoS, with deterministic bounds on the maximum delay and jitter on each video frame. Detailed simulations of an IPTV distribution system, multicasting several hundred high-definition IPTV video streams over several essentially saturated IP backbone networks are presented.