The book states seven principles and treats them as the whole of its teaching. They are worth listing plainly, since the book is far more often invoked than read, and since dating them to 1908 rather than to ancient Egypt changes what they are.
1. Mentalism, "The All is Mind; the Universe is Mental." The ground claim, and the one that makes the rest work: reality is fundamentally mental, so thought is causal. This is New Thought's central doctrine, not a Hermetic one.
2. Correspondence, "As above, so below; as below, so above." The one principle with a genuine old pedigree, since the phrase paraphrases the Emerald Tablet, though that text is a medieval Arabic work rather than an ancient Egyptian one.
3. Vibration, "Nothing rests; everything moves; everything vibrates." Stated in language borrowed loosely from nineteenth-century physics, and used to argue that raising one's 'vibration' changes one's circumstances.
4. Polarity, "Everything is dual; everything has poles." Opposites are held to be the same thing in different degree, so that hate and love, or heat and cold, differ only in position on a single scale.
5. Rhythm, "Everything flows, out and in; everything has its tides." A pendulum-swing between the poles, which the adept is said to escape by rising above the swing rather than being carried by it.
6. Cause and Effect, "Every Cause has its Effect; every Effect has its Cause." Offered as a law of universal determinism, with 'chance' recast as a name for unrecognised causes, and the adept as one who becomes a cause rather than an effect.
7. Gender, "Gender is in everything." A masculine and feminine principle held to operate on every plane, mental and spiritual as well as physical, and explicitly distinguished by the authors from sex.
The set is symmetrical, memorable and quotable, which is much of why it spread. None of the seven is found in the actual Hermetic treatises, which survive and can be compared; the framework is an early-twentieth-century American construction given an ancient frame.