1. I will learn a piano. This makes no sense. You can learn 'a song' or you can learn 'a piece of music', for example, but you can't learn 'a piano'. 'A piano' is the physical object. You would say 'There is a piano in the lounge', for example. You can't 'learn' an object. 2. I will learn the piano. 3. I will learn piano. These are both fine. Both of these refer to the skill of playing the instrument.

Numbers two and three are natural. The word 'the' is used when indicating a specific noun. The word 'a' or 'an' indicates a non-specific noun. So sentence one would be: I will learn an instrument. (Which instrument? The piano. But because 'the piano' is not stated in the sentence, we use an indefinite article such as 'a' or 'an'.) I will learn the piano. (Here we reference a specific instrument, the piano. Because we reference a specific noun we use the definite article 'the'.)