General:
* Acquiring knowledge
* Expanding one's horizons
* Gaining understanding
* Enrichment
* Exploration
* Developing skills
* Education
* Self-improvement
* Growing
* Evolving
More specific:
* Studying (formal learning)
* Researching (focused inquiry)
* Experimenting (hands-on learning)
* Mastering (achieving proficiency)
* Assimilating (absorbing new information)
* Internalizing (making knowledge part of oneself)
* Cogitating (thinking deeply about something)
Informal:
* Picking up new things
* Soaking it all in
* Broadening one's perspective
* Trying something new
The best word will depend on the specific situation and the tone you want to convey.