Operations is the building in the middle of your starbase. Nothing else on your base can be upgraded above your Operations level. Most new buildings stay locked until Operations reaches a set level.
At Ops 1 you have Operations, the Academy (where officers stay), Parsteel Generator A and Warehouse, Drydock A and Defense Platform A.
Ops 2: Parsteel Generator B. Ops 4: the R&D Department. Ops 5: the Shipyard, the Tactical Deck and Drydocks B to F. Ops 6: Tritanium Generator A and the Tritanium Warehouse. Ops 8: the Shuttle Bay. Ops 9: the Astronautics Studio. Ops 10: Dilithium Generator A, the Dilithium Warehouse and the Refinery.
The R&D Department (Ops 4) unlocks new ships, buildings and technologies. The Shuttle Bay (Ops 8) lets you send officers on Away Team Assignments. The Refinery (Ops 10) processes raw ore, crystal and gas. The Astronautics Studio (Ops 9) researches ship hulls before the Shipyard can build them.
Ops 12: Defense Platforms B to F. Ops 14: the three resource Vaults. Ops 15: the Treasury, Defense Technologies, the Holodeck and the Command Center. Ops 16: the Exocomp Factory and the Independent Archives. Ops 18: Tritanium Generator C and the Ship Hangar. Ops 19: the Court of Q. Ops 20: Dilithium Generator C, the Scrapyard and The War Room.
Drydocks B to F all unlock together at Ops 5. Then there is a long gap. Drydock G unlocks at Ops 30 and Drydock H at Ops 35. Plan your fleet around the ships you have, not around new slots.
Most core buildings cap at level 80. These include Operations, generators, warehouses, drydocks, the Shipyard and the Refinery. The Tactical Deck, EPS Distributors, Exographic Targeting Arrays, plasma harvesters and plasma vaults cap at level 34. Finish those once.