I have two questions and I hope someone can help me.
1.) After I registred at a bitcoin exchange, I bought bitcoins (june 2015) I received a Bitcoin address and this contained the 34 characters as mentioned in the book.
I did not generate or receive a private key of 64 characters.
However I did get, a so called Identifyer. The Identifyer is 36 characters instead of the 64 mentioned by Mr Popper.
2.) If the identifyer is the equivalent to the private key, should I worry that this key was send to me via email by/via a third party.
Thanks for any input
Mr. Popper's description is correct, addressed you create using a client such as bitcoin-qt or electrum or even blockchain.info have a public address and a corresponding private key.
However, as others have pointed out, your account at the exchange does not give you access to a private key. As many old hands here like to say, "If you don't control your private key you don't own your bitcoins."
If you create a wallet in a client or online wallet like blockchain you can instruct the exchange to send your coins to one of those addresses, then you'll have the address and private key.
As long as your exchange is honest it is not functionally an issue, but they have your coins, you have a claim on them for your coins.
I would not worry too much about the identifyer as long as your exchange account is protected by another system, e.g. password, two factor authentication.
Good Luck!