Is the transaction pool global or local? I can't find anything in the web about that topic. 
Do all the miners have one global pool filled with transactions, i. e. Miner 1 takes Transaction 1 into his candidate block, so Transaction 1 won't be in the transaction pool anymore.
Or does each miner has a local pool filled with transactions, so that each miner can take Transaction 1 into his transaction pool. 

If my question is unclear, I will try to describe it better. 
I hope someone knows a good reference to that topic.
Do all the miners have one global pool filled with transactions


Different full nodes have a different version of the mempool. Transactions are broadcasted to the bitcoin network on a best effort basis. If a transaction never reaches a node, it would not include it in the mempool. It would not learn about this transaction until it is included in the block by another miner. 


  Miner 1 takes Transaction 1 into his candidate block, so Transaction 1 won't be in the transaction pool anymore, Or does each miner has a local pool filled with transactions, so that each miner can take Transaction 1 into his transaction pool.


The second part is correct. Every miner creates their own candidate blocks using transactions from their own mempool. In case a miner is affiliated to a managed pool, the pool operator creates a block template (by including the transactions) and sends the header to the respective miners that are attached to the pool.