Convincing modulation is one of the strongest resources that a composer can use to achieve an impact on listeners. Also, modulation is a very important resource for achieving variety. Because of this, every longer composition contains modulations.
Modulation is a change of the current tonality. We deliberately say a change of the current tonality instead of a change of the current key. The reason is when the current key changes to its parallel key, the tonic stays the same and this is not considered a modulation but a change of the mode. For instance, when the C major key changes to the C minor key, this is not a modulation but the change of the mode. The difference between the tonality and the key was described in chapter Tonality and key.
When the tonality changes, the key also changes. Therefore, when annotating harmony, we must annotate the new key when a modulation occurs.
In the following chapters, we shall first explain tonicizations which look similar to modulations but are a different concept. Then we shall focus on modulations.