Short answers, pulled from the story.
A property tax is an ad valorem levy on the value of a property expressed as a percentage or per mille. The government appraises the monetary value of each property and assesses the tax in proportion to that specific appraisal value.
The first ever tax records date back about six thousand years BCE found in soil tablets within the city-state of Lagash now in Iraq. This system called bala rotated monthly so one particular area of the city was taxed making the task less difficult.
France imposes a local property tax known as taxe foncière payable by all owners of real estate located within its borders. The owner must pay the tax due each year from taxpayers who own property on the 1st of January of the tax year.
Places without property tax include China where government owns all lands and does not tax homeowners. American Samoa Palmyra Island and Kingman Reef have no tax on private land.
Germany exempts entities from public sector using property exclusively for public purposes only while non-profit organizations receive full exemption. Sweden exempts newly constructed single-family dwellings and owner-occupied flats for valuation year after 2012 from municipal property tax for first 15 years.