Hermes Trismegistus is accredited with the name Trismegistus, meaning the "Thrice Great" or "Thrice Greatest" because, as he claims in The Emerald Tablet of Hermes Trismegistus, he knows the three parts of the wisdom of the whole universe. The three parts of the wisdom are Alchemy, Astrology, and Theurgy.
Alchemy - The Operation of the Sun - For Hermeticism, Alchemy is not the changing of physical lead into physical gold. Rather, one attempts to turn themselves from a base person (symbolized by lead) into an adept master (symbolized by gold). The various stages of chemical distillation and fermentation, among them, are metaphorical for the Magnum Opus (Latin for Great Work) performed on the soul.
Astrology - The Operation of the Moon - Hermes claims that Zoroaster discovered this part of the wisdom of the whole universe, astrology, and taught it to humanity. In Hermetic thought, it is likely that the movements of the planets have meaning beyond the laws of physics and actually holding metaphorical value as symbols in the mind of The All, or God. Astrology has influences upon the Earth, but does not dictate our actions, and wisdom is gained when we know what these influences are and how to deal with them.
Theurgy - The Operation of the Stars - There are two different types of magic, according to 'Giovanni Pico della Mirandola's, Apology', completely opposite of one another (see Principle of Polarity below). The first is "Goetia", black magic reliant upon an alliance with evil spirits (i.e. demons). The second is "Theurgy", Divine Magic reliant upon an alliance with divine spirits (i.e. angels, archangels, Gods).
Theurgy translates to "The Science or art of Divine Works" and is the practical aspect of the Hermetic art of alchemy. Furthermore, alchemy is seen as the "key" to theurgy, the ultimate goal of which is to become united with higher counterparts, leading to the attainment of Divine Consciousness.
The Hermetic Principles
Note: I have tried to present these in a manner that they may be understood by everyone, as when I was learning about the Hermetic Laws they were couched in extravagant terms designed to be inaccessable to the average person. While I may in some cases have over simplified them, there are plenty of sites available online which have the full (if confusing) definitions for those who desire a deeper understanding of the topic (see sources and Resources for some of these sites).
The Principle of Mentalism.
"The All is Mind. The universe is mental -- held in the Mind of the All."
This basically means that our reality is in the mind of "God" (God being in this sense the creator of all - not a particular religious entity) and from that reality we create nd understand our own individual reality from what we perceive and how we perceive it.
The Principle of Correspondence.
"As above, so below; as below, so above."
In the various levels of reality: physical, mental, and spiritual, this principle shows that what happens on any level of reality happens on all the others (eg if you are stressed - mental, you become ill - physical, which weakens your auric field - spiritual).
This is however more often used in Paganism in a magickal sense - the microcosm and the macrocosm. The microcosm is oneself, and the macrocosm is the universe. That within each lies the other, and through understanding one (usually the microcosm) you can understand the other. By affecting one you can affect the other (one of the basic principles of sympathetic Magick)
The Principle of Vibration.
"Nothing rests; everything moves; everything vibrates."
If you have read anything about the Laws of Attraction this is the principle to which that refers. (this is often expressed in Paganism as "positive attracts positive - negative attracts negative") Within Magick, we use this principle by visualising and putting our energy into that which we desire we send out the energy of that desire which in turn is attracted back to us bringing that which we desire.
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."
Good and bad, negative and positive, light and dark, male and female are simply two sides of the same coin - neither can exist without the other. (A most simple explaination of this is; hot and cold - these are both extremes yet they are both just different degrees of the same thing, temperature. Where does hot finish and cold start? There is no beginning nor end they simply are of the same source.).
The Principle of Rhythm.
"Everything flows in and out; 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." Between the two poles which exist in accordance with the Principle of Polarity, there is always an action and a reaction, an advance and a retreat, a maximum and a minimum, (all the various degrees in between the extremes and energy moves bewteen them - consider day flowing into night flowing into day, flowing into night in and endless tide.)
The Principle of Causation.
"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." This simply states that for every action there is a reaction. It is said that the 'common' people float along on the causal plane their reactions a reflection of action (causation), while the 'spiritual master' moves above the Causal plane to the Effective plane - that is rather than reacting to an action outside of themselves - they, become the action and create reactions oin the world around them.
The Principle of Gender.
"Gender is in everything; everything has its Masculine and Feminine Principles; Gender manifests on all planes." This is simply another reflection of polarity, everything contain a degree of extremes (such as hot and cold) but everything also contains a degree of gener (masculine and femine - on every plane - mental, physical, and spiritual)
Magic, although a very powerful force, is not omnipotent. There are certain natural laws to which it must conform and certain limits that it may not exceed (at least, thus far). Many Magi struggle to surpass the known limitations of magic, and anyone which succeeds in exceeding one of these infamous limits shall be secured a place of honor in the Order's history. Presented here is a concise alphabetical list of the major laws and limits of Hermetic magic, codified by Bonisagus and the other founders in the Dark Ages (some appear in 4th Edition rules, pages 67-68, while others are House Rules). Magi are taught this list during their apprenticeship, and many Houses require them to be recited as part of their Gauntlet (with the notable exception of House Bonisagus, which struggles to surpass the laws and holds that acknowledgement of these 'temporary' limits enslaves them to the limits).
The four humors of the human body, phlegm, blood, bile, and black bile (which reflect the cold and moist, hot and moist, hot and dry, and cold and dry aspects of the body respectively), must remain in balance to maintain good health. An excess or deficiency of any single humor may invite poor health or possession by a foreign spirit.
Magic cannot affect a distant or unseen target without the use of an arcane connection to the specific target. Such connections must be valid, and most are not permanent.
By touching a spirit (or other intelligent entity, including demons), it is possible to 'become' that particular spirit, utilizing its powers. However, such unification of identities (also referred to as 'possession') may be difficult to reconcile or ultimately reverse, as once such a link is established the spirit may make use of the connection to suit its own ends, and particularly strong spirits may subsume the identity of the magus practitioner altogether.
Once whole, always whole (things that were once in contact with each other may continue to interact after their separation). This law is manifested in Hermetic magic with the use of arcane connections. Emphasis is on objects or people that have been in physical contact, for example fingernails or hair. But, such connections are only viable until the person to which they are connected cuts their hair or fingernails again (i.e., a lock of hair from a 16-year old lad will not prove effective when the boy is a 21-year old man). When a more durable connection is desired, blood is preferred, as it retains its connection to the target indefinitely. See the Limit of Arcane Connections and Erosion of Arcane Associations for more about their use.
Magic cannot create or alter anything permanently without the expenditure of pure magical energy (such energy has been categorized by Bonisagus and is termed 'vis' or 'colour', and is normally associated with either the 15 Hermetic Techniques & Forms or a specific lineage of magic). Further, vis cannot be created by magic, and the mystical association of any vis employed in Hermetic magics must conform to some degree with the nature of its intended use (e.g., Aquam, Terram, or Muto vis must be used to power a spell designed to transform water into stone).
No magic can overcome the power of the Highest Divinity or the deceptions of demonic powers. This includes affecting the result of a miracle, the manipulation of the mind or body of someone buried in piety by the Church, altering someone's true faith, detecting the presence or illusions of a demon, or the purposes of such illusions.
When an arcane connection is employed in the casting of a spell, a small portion of the connection is permanently eroded by the spell and rendered useless (the nature of such erosion depends on connection's physical manifestation). For example, fingernails may crumble to dust, or blood may dry-up. The quantity of the arcane connection that erodes and number of spells that may be cast from a particular connection before it is destroyed depends upon the physical manifestation of the source, and a Finesse roll by the Magus practitioner (e.g., a Storyguide may rule that a small pool of dried blood is sufficient to facilitate the casting of up to 3 Hermetic spells, formulaic or spontaneous, but each time a Magus employs the blood in one of her spells she must make a Finesse roll with an ease factor set by the Storyguide). If a Magus botches this roll, the arcane connection is likely ruined or destroyed prematurely.
It is impossible to alter or determine something's essential nature. This concept encompasses the ability to halt or reverse natural aging, perceive the machinations of a demon, and in game terms the revocation of Twilight or Decrepitude Points, the Heart-Shape of a Bjornaer Magus, or the creation or destruction of any supernatural aura.
Our mundane, human senses (i.e., sight, taste, touch, smell, hearing) are only capable of revealing part of true reality. Although it may be possible to extend and modify these senses with magic, they are still ultimately bound by these constraints and remain imperfect.
An unbroken circle drawn into the ground inscribing the Magus can serve to protect the Magus (who remains standing within it) by preventing an entity from entering the area denoted by the circle. Stepping across the circle boundary or distrubing its integrity breaks its power. Pentagrams are perhaps the best known of these circles, drawn to protect the magus from malicious demons, which are often summoned by implementation of the Law of Names.
Magic cannot affect anything above or including the lunar sphere (the 'high' air). Magic is always limited to manipulations of the middle and lower air.
Knowing the true name of a phenomenon or entity gives you control over it. This Law is particularly associated with demons and their ilk. A subset of this law, the Law of Words, expands this concept to include those words which are able to change and influence particular inanimate objects, plants, and places. Such words are often closely guarded secrets by ancient and powerful creatures and faeries.
The behavior or natural creatures, objects, or phenomena will persist according to their inherent temperament without the direct influence of subverting magics. The Law is important because it applies even if the natural form was conjured or summoned with magic (e.g., flames will burn and wolves will hunt and eat, each according to their own nature, even if they are magically conjured, and these effects will persist after the magic that created them subsides).
It is impossible to affect an immortal soul with magic (e.g., influencing the destination of someone's soul after death, creating true human life, or resurrecting the dead).
That which seems alike, is alike. Hermetic Magi often make use of this law, manifested in the use of spell foci (e.g., using a bird's feather to invoke flight, or snapping a bone to cause someone's arm to break).
Magic cannot alter the passage of time, nor can it affect anything in the past (though it may be possible to view the past). The only manner in which magic can affect the future is by making changes in the present.