The crystal structure type, ceramic microstructures, and dielectric properties of BaTi1-xGaxO3-delta (BTG) (0 <= x <= 0.15) ceramics prepared by the mixed oxide route have been investigated. X-ray diffraction shows the room-temperature crystal structure of BTG changes from tetragonal (t-BT; space group P4mm) to hexagonal (h-BT; space group P6(3)/mmc) at x similar to 0.04. These results are also confirmed by electron diffraction and dielectric measurements. For x > 0.12, a secondary phase isostructural with Ba2TiO4 is detected. Scanning electron microscopy (SEM) reveals three distinctive ceramic microstructures dependent on the firing temperature. BTG compacts fired at 1350 degrees C consist of fine (2-3 mu m) equiaxed grains within a narrow grain size distribution, whereas either large anisotropic or large (100-300 mu m) rounded grains embedded in a fine-grained matrix are observed for ceramics fired at 1400 degrees and 1450 degrees C, respectively. Transmission electron microscopy (TEM) of BTG (x=0.04) ceramics reveals some grains exhibiting both ferroelectric domains and stacking faults, which appear absent in ceramics with x >= 0.06. Ga-enriched grain boundaries were also revealed by energy dispersive spectroscopy (EDS) analysis. Dielectric measurements show the room-temperature relative permittivity, epsilon(r), for x <= 0.03 to be similar to 1500-2000 and that the Curie Temperature, T-c, decreases at a rate similar to 8 K/at.%, whereas the room-temperature epsilon(r) for h-BTG with x >= 0.06 decreases continuously with x from similar to 80 to similar to 65. h-BTG ceramics show a strong decrease in epsilon(r) with increasing temperature in the range 125-425 K, suggesting the possibility of a phase transition below 125 K.