Bitcoin is built atop the shoulders of the early P2P file sharing protocols. And the history of P2P file sharing starts with the grandfather of all massive P2P protocols, Napster.
Without public key cryptography, Bitcoin would be impossible. It lays the foundation for digital identities and cryptographically enforced property rights.
To understand Bitcoin's consensus mechanism and the concept of proof-of-work, we first have to understand Hashcash.
Merkle trees magically represent arbitrary amounts of data with a constant amount of space.
The most important building block for any cryptocurrency is the hash function.