A student recently wrote this sentence in an essay:

The headquarter is in Stuttgart.

This is a common mistake. The correct word is headquarters.

Even when people choose the right word, they often get the grammar wrong.

The company’s headquarters are in Stuttgart.

The problem is that there is only one headquarters, so using “are” is incorrect. We are fooled by the “s” at the end (native speakers included by the way).

The correct sentence is:
The company’s headquarters is in Stuttgart.

What if there is more than one company or more than one headquarters?
The companies’ headquarters are Stuttgart.