A solid titanium catalyst component which is disclosed in the above-cited British Pat. No. 1,433,537 and has the surface area specified hereinabove can be synthesized, for example, by adding about 3 to about 7 moles of a lower alcohol such as ethanol to 1 mole of magnesium chloride, reacting the adduct with an amount of an organoaluminum compound which is sufficient to react with the alcohol, and