You should transcribe each flight into your own logbook and also get that signed by the CFI / FTO on completion of the course.
As it is also getting towards the end of the year you might like to think about keeping an annual total as this can make it easier in years to come to keep a tally of your hours.
Some airlines will also keep a total of your hours but it is YOUR licence and therefore it is also YOUR responsibility to keep a log of your hours - including Duty hours - to ensure that you comply with the Duty / Flying hour limitations.
HWB