The 7 Hermetic Principles come from a foundational book within the realm of the Occult entitled The Kybalion: Hermetic Philosophy. The Kybalion was published in 1908 and is based on the teachings of Hermes Trismegistus.
The 7 Hermetic Principles listed in the Kybalion are considered by many groups to be the foundational beliefs for how magic works. While it is not necessary to "know" or believe in all 7 principles, hermeticism plays a huge role in the history of magic and the occult. The principles are as follows:
"The Seven Hermetic Principles, upon which the entire Hermetic Philosophy is based, are as follows:

1. The Principle of Mentalism.
"THE ALL IS MIND; The Universe is Mental."--The Kybalion.
2. The Principle of Correspondence.
"As above, so below; as below, so above."--The Kybalion.
3. The Principle of Vibration.
"Nothing rests; everything moves; everything vibrates."--The Kybalion.
4. The Principle of Polarity.
"Everything is Dual; everything has poles; everything has its pair of opposites; like and unlike are the same; opposites are identical in nature, but different in degree; extremes meet; all truths are but half-truths; all paradoxes may be reconciled."--The Kybalion."
5. The Principle of Rhythm.
"Everything flows, out and in; everything has its tides; all things rise and fall; the pendulum-swing manifests in everything; the measure of the swing to the right is the measure of the swing to the left; rhythm compensates."--The Kybalion."
6. The Principle of Cause and Effect.
"Every Cause has its Effect; every Effect has its Cause; everything happens according to Law; Chance is but a name for Law not recognized; there are many planes of causation, but nothing escapes the Law."--The Kybalion."
7. The Principle of Gender.
"Gender is in everything; everything has its Masculine and Feminine Principles; Gender manifests on all planes."--The Kybalion.

You can read the full Kybalion at Sacred-texts.com! Sacred-texts is a wonderful resource full of much of the necessary literature you would require for your magical and occult studies.

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