Why the atmosphere is thinner over the poles (600km) while the average is 800km? Is it thicker somewhere else and what's the reason for this? Thank you for your help! This is something that I didn't understand during my geography class.

It's because the earth rotates.

Actually, Atmosphere plays a very good important to us all Humans, the reason why the Atmosphere is thinner in both North Pole and South Pole because the climate affects the Gases in the Atmosphere, mainly the reason because the temperature there is below freezing point the tendency is the Gases stay at stationary movement and suspending their movements remember that when the temperature reaches the 0 degrees celcius all the movements of molecules becomes stationary and suspends making each atom of each gas is inactive to produce movement and their reactions also., so iend this but you can check from other resources thanks and i hope this has a lot information to you

Isn't it the same reason the earth is not a sphere, but actually "fatter" round the equator?

Because like Mr Skeptic said: it spins, it's quite intuitive.

remember that when the temperature reaches the 0 degrees celcius all the movements of molecules becomes stationary and suspends making each atom of each gas is inactive to produce movement and their reactions also

 

Um, no. Molecules do not cease moving at 0 ºC. You're thinking of absolute zero, which is -273.15 ºC, or 0 K.

He did bring up an interesting point though. A change in the temperature of air would make it denser, which would make the atmospheric layer thinner but denser, and slightly increase barometric pressure. Perhaps an effect of global warming would be a slight decrease in barometric pressure? I doubt it would be noticeable though.

Its colder there over the poles, most of air particles like dust and water freeze, grow in size, become heavy and drop down with snow.

Air pressure is nearly the same at the poles and the equator (about 1 bar).

 

Pressure is simply the weight of the atmosphere pressing down on us (units of pressure are Newton per square meter). So cold air, being more dense, does not require the same volume to create the same pressure.

 

Temperature is not the same at the poles and the equator.

 

Assuming that the temperature at the poles is a uniform -10 deg C, and at the equator it's +30 deg C, then a gas at the pole would be about 15% denser.

 

Obviously it is not so simple, because temperature fluctuates from day and night, and also it is colder when you go up in the atmosphere... but the 15% I just calculated comes close to explaining the difference between 600 and 800 km.