I purchased the game via PayPal yesterday, but I still haven't revieved an E-Mail containing the serial number, but strangely, I haven't seen the purchase in the PayPal history either.

Perhaps you did something wrong or something else went wrong during the PayPal action.

Do you have your PayPal account for a while now? Because if it is the first time you have a PayPal account, you need to wait three days until it is 'verified'. Then, you will receive two payments on your real bank account (the one that is linked). These two payments have to be transferred back to your PayPal account. Then your account is verified. Always verify your PayPal account. You can check the status on your PayPal transfers page.

Other than that, I would wait two days and if nothing has happened after that, just restart the PayPal payment (try to purchase the game again etc.). However, only do this when nothing has happened.

If you don't the purchase in your PayPal history, I think you should contact to their support service.