How many block chains exist? I´m beginner and I understood there is an unique huge common block chain to be used by world wide and there a several different crypto currencies types by  running on that . Am I correct?  Thank you to all
@Davide's answer is correct but I expand the explanation a bit particularly regarding the blockchain.


  I´m beginner and I understood there is an unique huge common block chain to be used by world wide


A crypto-currency like bitcoin requires people to run the bitcoin software that makes the whole system work; it is a Peer-to-Peer (P2P) network and each machine running the software is called a node.** The primary incentive for people to run nodes is that they are getting rewarded with bitcoins via a process called mining explained here and here. 

A blockchain (aka ledger) is a data structure (think of it as a file in your computer) that stores a history of all the transactions (actually groupings of transactions, called blocks, i.e. forming a chain of blocks) that took place in the network. Currently, it is around 65 GBs big and it is getting bigger with time as new blocks (of transactions) are added. Each node has a copy of the blockchain which is the same in all nodes via a consensus process enforced by computer algorithms.

Thus, in bitcoin, there is one common blockchain with copies in each node.


  and there a several different crypto currencies types by running on that . Am I correct? Thank you to all


No, other crypto-currencies make use of different software, form their own P2P network and have their own blockchains. Similarly, those networks will have a common blockchain and each node will have a copy. 

This is a simplified/high-level view but I hope it clarifies things a bit.

** Users that just want to use bitcoin do not need to run a node.