Learn Portuguese (Portugal): Eu hei de terminar o meu doutoramento e dominar esta tecnologia. - I will finish my doctorate and master this technology.

While vou terminar simply means "I am going to finish" (a standard future plan), the structure haver de + infinitive adds a strong layer of determination, intention, or personal promise. Using hei de terminar is like saying "I shall finish" or "I am absolutely determined to finish."

Does the hei de apply to both terminar and dominar?

Yes! You don't need to repeat hei de after the e (and). Because both terminar (to finish) and dominar (to master) are left in the infinitive, the single hei de at the beginning naturally applies to both of those actions.

Why is there an o before meu doutoramento?

This is a quick refresher on possessives: in European Portuguese, it is standard to place a definite article before a possessive word. Since doutoramento is a masculine singular noun, you use o. It literally translates to "the my doctorate", which is the most natural way to say "my doctorate" in Portugal.

Is doutoramento the standard word for a PhD?

Exactly. In Portugal, doutoramento is the standard term for a doctorate or PhD degree. If you consume Brazilian media you might hear doutorado instead, but in European Portuguese, doutoramento is the word you want.