I recently read the bitcoin paper. Some key notes

An electronic coin is a chain of digital signatures. Each owner transfers the coin to the next by digitally signing a hash of the previous transaction and the public key of the next owner and adding these to the end of the coin.

Proof-of-work involves scanning for a value that when hashed (such as) with SHA-256 the hash begins with a number of zero bits. The average work required is exponential in the number of zero bits required and can be verified by executing a single hash.

(bitcoin) implements proof-of-work by incrementing a nonce in the block until a value is found that gives the block’s hash the required zero bits.

proof-of-work difficulty is determined by a moving average targeting an average number of blocks per hour. Difficulty is increased if they are generated too fast.

Incentive: By convention, the first transaction in a block is a special transaction that starts a new coin owned by the creator of the block.