Formal:
* Grasp: This word emphasizes the act of seizing or taking hold of an idea.
* Comprehend: This word implies a thorough understanding.
* Perceive: This word focuses on the act of becoming aware of something.
* Apprehend: This word suggests a clear and accurate understanding.
* Assimilate: This word implies that the information is fully incorporated into one's knowledge.
Informal:
* Get: This is a casual way to say "understand."
* Figure out: This implies a process of working something out.
* See: This is a simple and direct way to say "understand."
* Catch on: This suggests that one is beginning to understand something.
* Wrap one's head around: This emphasizes the effort required to understand something complex.
The best word to use will depend on the specific context and the desired level of formality.