Concept:
The Bayer process is used to extract alumina from bauxite ore.
Step 1: Bauxite is an ore of aluminium.
Step 2: It contains hydrated aluminium oxide along with impurities.
Step 3: In the Bayer process, bauxite is treated with sodium hydroxide to dissolve alumina.
Step 4: Alumina is then precipitated and calcined to obtain:
\[
Al_2O_3
\]
Therefore, Bayer process is used to produce:
\[
\boxed{Al_2O_3}
\]