General synonyms:
* Acquire
* Master
* Grasp
* Comprehend
* Understand
* Discover
* Absorb
* Pick up
* Take in
More specific synonyms:
* Study: To learn formally, often in a classroom setting
* Memorize: To learn something by heart
* Practice: To learn by repeated doing
* Research: To learn by investigating and gathering information
* Explore: To learn about something new and unfamiliar
* Educate: To teach someone
* Train: To teach someone a specific skill
The best synonym to use will depend on the specific situation and what you want to emphasize.