Since Aluminum is already answered here is the process for titanium in short:
The most common titanium containing minerals are Rutile and Ilmenite
Ilmenite is first turned into Titanoxide (Rutile is one already) by extracting the iron part, for example with sulfuric acid.
Then under hot temperatures it’s reacted with chlorine and coal to titantetrachloride (and carbonmonoxide).
In the last step you remove the chlorine again by reducing it with liquid magnesium or sodium
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