The best advice when booking your Kilimanjaro climb is to book ahead as much as possible. If you book long in advance you will quite often be able to get cheaper flights and better deals on your tours. You will have enough time to train and prepare for the climb.
Booking in advance will furthermore provide confirmation and reassurance of the tour. It also reduces the possibility of not being able to get onto the tour you want, due to lack of spaces and some of the vaccinations you will need to take in time to become effective.
Where possible, try to book at least 3-6 months in advance.
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