The World of Warcraft team has released the dungeon and raid schedule for the months following Legion's release. The Normal and Heroic versions of all dungeons will be open from August 30th, Legion's launch day, with Mythic versions coming along the next week after reset.
The rest of the schedule is:
Tuesday, September 20th - Emerald Nightmare raid opens for Normal and Heroic. Mythic Keystones will begin to drop to increase challenge and rewards from Mythic-level dungeons
Tuesday, September 27th - Mythic Emerald Nightmare raid opens and the first Emerald Nightmare Raid Finder wing opens
Tuesday, October 11th - Raid Finder wing 2 of Emerald Nightmare opens
Tuesday, October 24th - Raid Finder wing 3 of Emerald Nightmare opens
Keep an eye on the World of Warcraft community site for more.