I am reading about the Merkle tree, I've read that in a block we store just the root of the tree. To check if a ttransaction is included in the Merkle tree we need to use the transaction's Merkle path. The question is where the Merkle tree is stored? How would a node given a path check if the leaf belongs to the Merkel tree?
The Merkle tree is not stored anywhere.
It is implicitly defined by the transactions in a block. Whenever needed, the portion of it that is needed is computed on the fly using the transaction identifiers.