Yes, houses and apartments freely; land requires a local company.
Costs on top of the price
1-4% · New build: 21% VAT is normally included in the developer price, buyer pays notary + ~1% legal; resale: 3% transfer tax (progressive on higher values) + notary + ~1% legal (GPG 4.01%).
Yearly property tax
Municipal, ~0.25-1% of assessed value (higher rates possible for tourist properties).