Your example is about grammar, and grammar is more of a skill or ability (gaining knowledge of grammar in this case). You would only 'learn grammar' from/for something, therefore the article a/the would apply to what you are learning from (the teacher, a book, that book). The application of a/the is dependent upon the situation, as 'a' can apply to any, regardless of the where/who/what. 'The' is more specific, referencing something specific that you may already be talking about earlier in the conversation. Your statements would not really fit as complete sentences alone. So it would either be along the lines of "I/he/she learns grammar from/during..." as an infinitive, or a different tense entirely such as: "I am/he is/she is learning grammar." "I have/he has/she has learned grammar."

We would never say simply, "I am learning a grammar." The word "grammar" *can* be used to mean "a textbook that explains the grammatical rules of a language," and in this case you could say, for example, "I am studying a Latin grammar" or "Yesterday I bought an English grammar." You still would not say, "I am learning an English grammar," since you do not *learn* a book but rather *study* or *read* one. But we can say, "I am learning grammar," often with an adjective in front of the word "grammar," as in the sentence "I am learning English grammar." We can also say, for example, "I am learning the grammar of English," which means the same thing.