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Preliminaries.- Some classes of locally convex spaces.- Ultrabarrelled, ultrabornological and quasiultrabarrelled spaces.- Order-quasibarrelled vector lattices.- Countably barrelled and countably quasibarrelled spaces.- ?-Barrelled and sequentially barrelled spaces.- Countably ultrabarrelled and countably quasiultrabarrelled spaces.- Countably order-quasiultrabarrelled vector lattices and spaces.- Order-quasiultrabarrelled vector lattices and spaces.