The differential forms approach also has the advantage over geometric algebra of being widely used by mathematicians and theoretical physicists, and perhaps increasingly used by physicists in general. If you're going to put in the effort to learn geometric algebra, learning differential forms instead would be much much more useful in opening up the literature to you. A 'lightweight' intro is [1].

[1] https://www.amazon.com/Electricity-Magnetism-Mathematicians-...