Cryptography, literally "secret writing", was originally the practice of encrypting a message so that only people who knew the secret key could decrypt it. In more recent years, the field of cryptography has expanded to cover all forms of cooperation without vulnerability in a world of mutually suspicious agents. Encryption provides cooperation without vulnerability because it lets you transmit your message through insecure channels without being vulnerable to them reading the message.
The field was revolutionized with the discovery of public-key cryptography by Whitfield Diffie and Martin Hellman, announced in their paper New Directions in Cryptography. Since then, a large variety of cryptographic protocols have sprung up including digital signatures, secret sharing, coin flips, bit commitment, zero-knowledge proofs, electronic cash and many more.
Unfortunately, the implementing cryptography has been limited export controls and patents. Worse, the cryptographic software that is available to users has notably poor usability. However, many of these issues have been or are being resolved and there is a bright future for cryptography ahead.
Bruce Schneier's Applied Cryptography is one of the key works in the field, covering the protocols, algorithms and source code by one of the leaders of the field.
Francis Litterio's introduction to cryptography includes links to important books and documents.