Assalaamu alaykum wa rahmatullaahi wa barakaatuhu. Can my mother sell my old books in order to free up space in the house without my consent?

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.

Your mother does not have the right to sell anything (of your possessions) without your consent, whether the objective is to free up space in the house or otherwise.

However, if she is the owner of the house, she may ask you to take them away to another place, because the owner has the right to legitimately dispose of his property as he wishes.

The Maaliki book of Fiqh Haashiyat-ad-Dusooqi reads, "The owner has the right to dispose of what he owns as he wishes."

So it is not permissible for her to sell them without your consent.

Allah knows best.