Formal:
* J'ai beaucoup appris. (I have learned a lot.)
* J'ai appris énormément. (I have learned tremendously.)
Informal:
* J'ai appris plein de choses. (I have learned a lot of things.)
* J'ai appris un max. (I have learned a ton.)
* J'ai appris pas mal. (I have learned quite a bit.)
To emphasize the effort:
* J'ai beaucoup appris grâce à... (I have learned a lot thanks to...)
* J'ai fait beaucoup de progrès. (I have made a lot of progress.)
To emphasize the knowledge gained:
* J'ai acquis beaucoup de connaissances. (I have acquired a lot of knowledge.)
* J'ai une meilleure compréhension de... (I have a better understanding of...)
You can also use different tenses depending on the context:
* J'apprends beaucoup. (I am learning a lot.)
* J'ai appris beaucoup ces derniers temps. (I have learned a lot lately.)
Remember to choose the phrase that best suits the situation and the level of formality required.