Learn Romanian: Voi studia știința.

The word voi is the future tense helping verb for "I" (I will). In the standard Romanian future tense, it is always followed by the infinitive (dictionary form) of the main verb without the word a. So, a studia (to study) becomes just studia.

Would it be wrong to say "voi a studia"?

Yes, it would be incorrect. Even though the dictionary form is a studia, you must drop the a when forming this standard future tense. It is always just the helping verb + the bare verb itself.

English just says "science", but Romanian says știința ("the science"). Why?

In Romanian, broad concepts and academic subjects usually take the definite article (the equivalent of "the" in English) when used in a general sense. The base noun is știință (science), and to add the "the", the final -ă changes to -a, making it știința.

Why does the word știința have a double 'i'?

That is simply how the base word știință (knowledge or science) is spelled. It comes from the common verb a ști (to know). The double 'i' preserves the root and creates a slightly longer "ee" sound.