I'm writing a paper for myself in order to understand how bitcoin works. I have a serious problem of understanding the transactions. According to definition of public key cryptography, Elliptic Curve Digital Signature Algorithm and Nakamoto's paper, a transaction consists of the previous transaction plus the payee's public key in the hash function, which is signed by payer's private key to confirm the change of owner rights. At least this is what I understand.
The definition of Transactions in bitcoin wiki is a little different than that. It also says that nothing in the network is encrypted. Could someone please explain me how a transaction works? Thanks in advance.
Those definitions don't conflict at all. Transactions involve signing and hashing, but encryption doesn't ever take place (unless you count signing as encryption, which may technically be correct). It seems that you pretty much understand it (other than the whole scripting part, but I'd ignore that until you understand everything else). Honestly, I'd suggest just looking at a few transactions over at Blockexplorer.com and let us know if you still have any questions.