The Avatamsaka Sutra is famous for its teaching of "unobstructed interpenetration", which can be explained by way of a famous image: the Jewel Net of Indra, "which has always been a favorite ... method for exemplifying the manner in which things exist":
Far away in the heavenly abode of the God Indra, there is a wonderful net which has been hung by some cunning artificer in such a manner that it stretches out infinitely in all directions. In accordance with the extravagant tastes of Deities, the artificer has hung a single glittering jewel in each "eye' of the net, and since the net itself is infinite in dimension, the jewels are infinite in number. There hang the jewels, glittering like stars of the first magnitude, a wonderful sight to behold. If we now arbitrarily select one of these jewels for inspection and look closely at it, we will discover that in its polished surface are reflected all the other jewels in the net, infinite in number. Not only that, but each of the jewels reflected in this one jewel is also reflecting all the other jewels, so that there is an infinite reflecting process occurring.... [T]his image ... symbolizes a cosmos in which there is an infinitely repeated interrelationship among all the members of the cosmos. This relationship is said to be one of simultaneous mutual identity and mutual causality.
[Cook 1973, p.1]
In Buddhism the Sutras are the sacred texts that contain the actual teachings of the Buddha in his own words. Each Sutra gives a time and place when and where it was spoken, and some idea of the circumstances, including who was there to listen.
The Avatamsaka Sutra was the very first teaching that the Buddha gave, still sitting on the spot where he attained enlightenment. Beings from across the earth and from across the Universe gathered in a great Cosmic Assembly to hear the first utterance of the Awakend One. Some people question the so-called "historicity" of the Avatamsaka Sutra and insist that it does not contain the words of the Buddha at all, and that it was written by others centuries after the Buddha had died. Technically speaking the Avatamska Sutra does not really make a "historical" claim so much as it claims to transcends ordinary space and time completely, not just in the meaning of the teaching it contains, but in the manner in which this teaching was delivered!
The Avatamsaka Sutra, which is also known as the Hua-Yen Sutra, therefore represents the most direct and complete expression of the Buddha's teachings. As such, this teaching is very advanced and difficult to understand, and so for the rest of his career as a teacher the Buddha tried various approaches to restating these teachings in ways that were more accessible.
A closely related Sutra is the Sutra of Perfect Enlightenment, which can be considered something like a Readers Digest Condensed Version of the Avatamsaka. The Sutra of Perfect Enlightenment became part of the standard core curriculum for study among Zen Buddhists in China and Korea, but for some reason it faded to relative obscurity in Japan. This might be because the Hua-Yen and Zen schools were, technically, rivals - but in China and Korea Zen Buddhism developed a more syncretic attitude toward rival schools than the (at least somewhat) greater sectarianism in Japanese Zen. This is not limited to Hua-Yen Buddhism, but is also reflected in the attitude toward Pure Land and Esoteric/Tantric teachings as well, which are far more seamlessly syncretized with both Chinese Ch'an and Korean Soen than they are in Japanese Zen.
There are three standard English works on the Avatamsaka/Hua-Yen Sutra:
Entry into the Inconceivable: An Introduction to Hua Yen Buddhism by Thomas Cleary
The Buddhist Teaching of Totality: The Philosophy of Hwa Yen Buddhism by Garma C.C. Chang
Hua-Yen Buddhism: The Jewel Net of Indra by Francis H. Cook [quoted above]
Two English language versions of the Sutra of Perfect Enlightenment (also known as the Sutra of Complete Enlightenment) are also available:
Complete Enlightenment: Translation and Commentary on the Sutra of Complete Enlightenment by Master Sheng Yen [this is far more accessible than the next one!]
The Sutra of Perfect Enlightenment: Korean Buddhism's Guide to Meditation (With Commentary by the Son Monk Kihwa) edited and translated by A. Charles Muller
Also, the wikipedia entry on the Sutra of Perfect Enlightenment is actually not too bad, and it talks briefly about it's relationship with Chinese Hua Yen Buddhism. That entry also contains a direct link to Charles Muller's English translation of the Sutra of Perfect Englightenment - including the complete text of Muller's brief but very informative Introduction.
But what about the Sutra itself?? The only English translation of the complete Avatamsaka Sutra is Thomas Cleary's 1,643 page tome, which has a list price of $100, but Amazon currently has it deeply discounted down to a mere $63. If you buy books by the pound, it's a pretty good deal:
The Flower Ornament Scripture: A Translation of the Avatamsaka Sutra Thomas Clearly.
I love google image searches, don't you? If you do a google image search on "avatamsaka" the very first hit is the beautiful picture of Samantabhadra Bodhisattva illustrating this post (taken from here). He is a key figure in the Avatamsaka Sutra, and like all Great Bodhisattvas and other "persons of note" he has his own wikipedia entry.