Parallelism means that words used in pairs or groups should all have the same grammatical form (verbs and verbs; nouns, nouns, and nouns; gerunds and gerunds, etc.) When using words or phrases with coordinating conjunctions or in a series, make sure that they follow the same grammatical structure.

For example,

Terry likes swimming and to dive. Terry likes swimming and diving. Terry likes to swim and (to) dive. I’m taking history, math, and chemical. I’m taking history, math, and chemistry.

(Incorrect: not parallel) (Correct) (Correct) (Incorrect) (Correct)

Sometimes repeated words, such as auxiliary verbs, can be deleted in parallel constructions.

I have been to Paris and saw the Eiffel Tower. I have been to Paris and have seen the Eiffel Tower I have been to Paris and seen the Eiffel Tower. Is she coming to the party or go to a movie? Is she coming to the party or going to a movie?

(Incorrect) (Okay) (Better) (Incorrect) (Correct)