The Stables is the mounted/cavalry training building; higher level unlocks higher mounted tiers plus training capacity/speed. Requires Keep 6 (Lv1-6 need only Keep 6), then matching Keep level from Lv7 to Keep 50; from Lv26 also Mine (and Tavern at Lv27/30/32/35), plus Archer Camp at Lv44/49; Lv40 also a Military Academy Mounted Formation research and Victory Column 2. Mounted tier unlocks: T2@6, T3@9, T4@11, T5@14, T6@16, T7@19, T8@21, T9@23, T10@25, T11@27, T12@30, T13@32, T14@35, T15@40, T16@45, T17@50. Blazon at Lv8. Key milestone: Duty Officer at Lv33 (the latest of the four training buildings; increases Mounted Training Speed and Capacity; ideal Oleg of Novgorod, John Adams, Stilicho). Costs match the others (Lv1 1,000/1,000; Lv25 ~11M/14M/15M/14M; Lv50 ~119B/152B/156B/152B). Speed +0% to Lv17, +30% at Lv18 to +610% at Lv50. For a bot: Stables gates cavalry tier and mounted training throughput; note the duty-officer slot arrives late (Lv33), so mounted training speed lags unless a general is hot-swapped in.
Original research source: Evony Guide Wiki