General synonyms:
* Create
* Design
* Devise
* Originate
* Conceive
* Develop
* Discover
* Forge
* Formulate
* Generate
* Produce
* Think up
More specific synonyms:
* Fabricate (to make or manufacture something)
* Pioneer (to be the first to develop or use something)
* Innovate (to introduce new methods or ideas)
* Conceptualize (to form a concept or idea)
The best synonym for "invent" will depend on the specific context.