According to the Swedish Tax authority's recommendations, a mileage logbook should contain:
odometer reading at the beginning of the year
odometer reading at the end of the year.
the car's registration number
current year
date and odometer reading at the start and end of each trip
how many kilometers the employee drives each trip
which address the trip started from and ended at
purpose of the trip
which places, companies or contact persons the employee has visited (not needed for private trips)
notes about the driver and refueling, etc.