In this book, we have tried to answer general questions that are fundamental to topological analysis applied to musical data: how should we associate a filtered complex with a given piece of music? What can such a representation contribute to musical analysis? How much does it help us to understand music? For example, is it able to classify several different styles? In this particular context, we focused on the symbolic representation of music, as opposed to audio and signal, and such a representation is given by MIDI files.