In this Russian verbs lesson for learners of the Russian language that are beginning to study cases, starting about 5:10 into this video there is information about the verb учить. This verb учить in Russian can mean both to study and to learn. The creator of Russian Plus talks about the Russian cases that apply to make this possible in this video.
There are other verbs discussed in this video. They series of three videos is great for language learners with some experience because he goes over aspects such as perfective and imperfective verbs and will list some different forms of each verb with different prefixes and suffixes. Beginning users might look cross-eyed at all the options. Advanced users can use it for review.
Here's a post at Tumblr with a lot of information about this same subject of learning and studying ... Verbs for ‘to learn’ and ‘to study’: учить, изучать, учиться, научиться and заниматься.