Ankh: An Ancient Egyptian symbol representing divine authority and power over life and death, therefore sovereignty, reincarnation, and the balance of polarities. The handle represents the masculine principle (Osiris), and the looped top represents the feminine principle (Isis).
Baphomet: An image designed by the nineteenth-century occultist Eliphas Levi, based on an idol that the Knights Templar supposedly worshipped. Levi's Baphomet is meant to be a symbol of the alchemical process and the synthesis of dualities.
Chaostar: In true chaote fashion, this symbol comes from a fantasy novel called The Eternal Champion by Michael Moorcock. It has been adopted by occultists as a symbol of Chaos Magic, a philosophical approach to magic that emphasizes experimentation and choosing one's own beliefs and perceptions. Its eight arrows make it resemble the Star of Ishtar, and represent infinite possibilities.
Cross: One of the most universal human symbols; versions of it appear in almost all cultures, and it represents all sorts of different things. In alchemy, it represents the balance of polarities, the four elements and quintessence. In Hinduism, the swastika is a cross that represents the Sun, good luck, and benevolence.
Elemental Symbols: The alchemical symbols for the four elements are triangles.
Earth: A downward-pointing triangle with a horizontal line through it. Earth represents stability, fertility, abundance, growth, health, rigidity, strength, fixation, health, and the physical world. It's associated with North and winter, and its properties are cold and dry.Air: An upward-pointing triangle with a horizontal line through it. Air represents intellect, insight, scholarship, communication, eloquence, commerce, travel, volatility, and the mental world. It's associated with East and spring, and its properties are hot and wet.Fire: An upward-pointing triangle. Fire represents expansion, sexuality, passion, desire, vitality, courage, willpower, success, compitition, destruction, power, purification, enlightenment, and the spiritual world. It's associated with South and summer, and its properties are hot and dry.Water: A downward-pointing triangle. Water represents change, love, peace, sleep, inspiration, empathy, healing, purification, primordial chaos, creativity, potential, resurrection, and the emotional world. It is associated with West and autumn, and its properties are cold and wet.
Eye of Horus: An Egyptian symbol, also called the wedjat, that represents the eye that the god Horus lost in his battle with Set. It was very often used as an amulet in Ancient Egypt, which would protect its wearer. It was especially used as protection for the dead, and as a healing agent.
Goetic Seals: Sigils from a grimoire called the Lesser Key of Solomon that are the insignias of the 72 demons who supposedly built Solomon's temple. There are many sigils representing spirits throughout this grimoire and others, but the 72 Goetic seals are the most famous.
Hieroglyphic Monad: A pseudo-alchemical symbol invented by John Dee, which he wrote an entire book to explain. It's a composite symbol representing the Moon, the Sun, the four elements, fire, and the universe at large.
Hexagram: A six-pointed star made of two overlapping triangles. Called the Star of David in Judaism. It is made of all four elemental symbols, and therefore represents the unification of the elements. It also embodies the occult maxim "As above, so below." The Unicursal Hexagram is the symbol of the religion of Thelema.
Kabbalistic Tree of Life: The central symbol of the Jewish esoteric system of Kabbalah. Each circle on the "tree" is a vortex of light called a sephiroth, and they represent emanations of God. At the top is Kether (the Godhead), Binah (Understanding), and Chokmah (Wisdom), in the middle is Chesed (Mercy), Geburah (Severity), Netzach (Victory), Hod (Splendor), and Tiphareth (Beauty), and at the bottom is Yesod (Foundation) and Malkuth (Kingdom). The process of spiritual ascension in Kabbalah involves metaphorically "climbing" the tree.
Leminescate (Infinity Knot): Represents eternity and the natural flow of all things, both polarity (the two bulbs) and unity. Often, it represents prima materia and the Principle of Mentalism (all the universe emanates from God), like the Ouroboros.
Labyrinth: A very old symbol of the path towards the divine, and also one's own subconscious mind. The difficult and confusing challenge of navigating the Otherworld or the Underworld, which is necessary to reach enlightenment and spiritual growth.
Mjolnir: The symbol of Thor's hammer in Norse paganism. It is an amulet of protection, strength, and rejuvenation.
Merkabah: Hebrew for "Chariot," a three-dimensional Star of David, a pyramid and inverted pyramid merged together. Represents the astral body and the ability to access higher planes of existence. It represents the faces of the Cherubim – lion (fire), ox (earth), man (water), and eagle (air). It also represents the duality of the masculine and feminine in alchemy. It is therefore a representation of alchemical union, and transmutation into the divine state. Metatron's Seal or Metatron's Cube is a two-dimensional version of it.
Om Symbol: A Hindu symbol, ॐ, representing a sound, AUM, that represents the entirety of the universe, the primordial cycle of creation and destruction, and the essence of reality. It is believed to be the first sound made in the universe, and the music of the spheres.
Ouroboros: A snake eating its own tail, representing the self-begotten, self-generative, and self-destroying nature of the universe. It also represents the Principle of Mentalism, the idea that the entire universe exists in the mind of God. It is primordial chaos and prima materia, from which all things come and to which all things return. It also represents the cyclical process of the alchemical Great Work and the repetition of solve et coagula.
Pentagram: One of the most ubiquitous occult symbols, associated with many different ideas in different contexts. In Western occultism it represents the four elements plus quintessence, and also represents equilibrium (because it divides the "perfect" ten in half). It's used as a protective amulet in grimoires. It's also the symbol for the religion of Wicca.
Planetary Symbols: Traditionally, the five planets that can be seen from the Earth with the naked eye, plus the Sun and Moon.
Sun: ☉ Represents spiritual perfection, individualization, completion, creativity, power, enlightenment, fame, luck, vitality, confidence, and happiness. In alchemy, it is considered masculine and its metal is gold. It's also a symbol of the rubedo stage.Moon: ☽ Represents transformation, emotion, protection, travel, imagination, dreams, madness, prophecy, intuition, and the subconscious mind. In alchemy, it is considered feminine and its metal is silver and quicksilver. It's also a symbol of the albedo stage.Mercury: ☿ A stylized caduceus. Represents intelligence and intellect, travel, healing, commerce, communication, memory, eloquence, divination, knowledge, and transmutation. In alchemy, it is considered androgynous, and is a symbol of the Philosopher's Stone and the entire Great Work.Venus: ♀ A stylized hand mirror. Represents love, sexuality, beauty, art, passion, peace, friendship, harmony, fertility, luxury, pleasure, generosity, and relationships. In alchemy, it is considered feminine and its metal is copper.Mars: ♂ A stylized shield and spear. Represents action, aggression, physical power, lust, conflict, victory, strength, virility, destruction, empowerment, and energy. In alchemy, it is considered masculine and its metal is iron.Jupiter: ♃ A stylized thunderbolt. Represents wisdom, justice, wealth, abundance, peace, expansion, joy, optimism, health, fame, good fortune, honor, and benevolence. In alchemy, it is considered masculine and its metal is tin.Saturn: ♄ A stylized sickle. Represents death, restriction, discipline, structure, endurance, time, frugality, longevity, stability, limitations and hindrances, binding, and banishing. In alchemy, it is considered masculine and its mental is lead. It's also a symbol of the nigredo stage.
Platonic Solid: Three-dimensional regular geometric solids, described by Plato in one of his dialogues and each associated with an element. The cube is made up of four squares, and represents Earth because it is solid and stable. The tetrahedron is made up of four triangles, and represents Fire. The Icosahedron is made up of twenty triangles, and represents Water because it rolls most easily. The octahedron is made up of eight triangles, and represents Air. The dodecahedron is made of twelve pentagons, representing Spirit and the entire universe.
Seal of Baphomet: An inverted pentagram with a goat's head arranged in its points, and Hebrew letters spelling out the word "Leviathan" arranged around the outside of it. Sometimes the names "Samael" and "Lilith" are arranged above and below the pentagram, between its points. It first appeared in a book called La Clef de la Magie Noire by Stanislas de Guaita in 1897. Anton La Vey adopted it as the official insignia of the Church of Satan, formally associating it with the taboo ideas that it was intended to represent.
Seal of Lucifer: A symbol from the Grimorium Verum, an eighteenth-century grimoire of the Solomonic tradition. It has increasingly gained presence as a symbol for Satan or Lucifer, being more specific than the ubiquitous inverted pentagram. It is sometimes used as a symbol for theistic Satanism.
Septagram: A seven-pointed star, sometimes called the "elvenstar." It's used throughout occult fields and means different things depending on the tradition. In Thelema, it's the seal of the goddess Babalon. In alchemy, it represents the seven planets or the four elements plus sulfur, mercury, and salt. I personally take it to represent the four classical elements, plus light, darkness, and anima (spirit).
Sigillum Dei: I first encountered this sigil on a Nox Arcana CD (literally, printed on the actual disk itself). It's the "Seal of God," which bestows divine power upon the magician. It originally comes from the Sworn Book of Honorius. John Dee adapted it into his own system of ceremonial magic.
Spiral: Another nigh-universal symbol that represents many different things in different context. Symbolizes the journey of the soul to the Source and also the expansion of energy from the Source. Represents moving in a cyclical motion that nonetheless progresses towards an objective, making it a synthesis of masculine and feminine energy. Also represents Spirit or quintessence.
Squared Circle: An alchemical symbol that represents the Philosopher's Stone. "Squaring the circle" means the same thing as "fixing the volatile," uniting the four elements of the material world (the square) into spiritual quintessence (the circle). It also represents the proportionality of the microcosm to the macrocosm.
Sulfur Cross: Alchemical symbols representing sulfur. Sulfur is the masculine principle in its "impure" form, a "seed" of metals that must combine with the feminine quicksilver (mercury) to form the Philosopher's Stone. It represents the mundane mind or consciousness. The version with the infinity knot, sometimes called the "Leviathan cross," became a Satanic symbol after Anton La Vey adopted it. This is probably because of the association between sulfur and hell, as in "fire and brimstone."
Tetragrammaton: The four Hebrew letters that spell the name of God, YHVH. Used almost ubiquitously in ceremonial magic, often inscribed on amulets or written into magic circles. Sometimes the actual word "tetragrammaton" will be used instead of the letters. Some Jewish and Christian mystics believed that the name contains the creative powers of God — should the name be pronounced correctly, it would allow the speaker to control the entire universe.
Triple Moon: A Wiccan symbol used to represent the Triple Goddess, a concept invented by Robert Graves. The waxing moon represents the Goddess in her Maiden form, the full moon represents the Goddess in her Mother form, and the waning moon represents the Goddess in her Crone form.
Triquetra: A nigh-universal knot symbol, best known as a feature in Celtic artwork. Symbolizes many different concepts in many different traditions. It is used as a symbol of the Trinity in Christianity, and the Triple Goddess in Wicca, or triplicities of goddesses (like the Morrigan) in Celtic reconstructionism. The triskele is a pinwheel-shaped variant.
Valknut: A Germanic symbol made of three interlocking triangles. It's unknown exactly what the symbol means, but it's probably related to Odin, because it is drawn next to depictions of him on his horse. It might have represented power over life and death and transition to the afterlife, similar to an ankh. It could also have represented Odin's possession of or protection over whatever it was drawn on. It's a common religious symbol among Heathens of various types (some more savory than others).
Zodiac Symbols: The twelve symbols of the Western Zodiac, which are all stylized representations of whatever the constellation is supposed to be. They are used to represent many different things in different traditions of occultism, and have many layers of planetary and astrological associations. They all have their own sets of correspondences and traits associated with them:
Aries: ♈︎ A cardinal Fire sign. Associated with independence, optimism, enthusiasm, courage, determination, ambition, and impulsivity. Ruled by Mars and affiliated with the first house.Taurus: ♉︎ A fixed Earth sign. Associated with security, subtlety, stubbornness, patience, persistence, generosity, laziness, and materialism. Ruled by Venus and affiliated with the second house.Gemini: ♊︎ A mutable Air sign. Associated with communication, intelligence, wit, adaptability, fickleness, and indecisiveness. Ruled by Mercury and affiliated with the third house.Cancer: ♋︎ A cardinal Water sign. Associated with compassion, moodiness, sensitivity, and emotional intensity. Ruled by the Moon and affiliated with the fourth house.Leo: ♌︎ A fixed Fire sign. Associated with confidence, loyalty, ambition, generosity, domineering tendencies, and vanity. Ruled by the Sun and affiliated with the fifth house.Virgo: ♍︎ A mutable Earth sign. Associated with precision, reliability, practicality, observational skills, fussiness, and inflexibility. Ruled by Mercury and affiliated with the sixth house.Libra: ♎︎ A cardinal Air sign. Associated with gracefulness, diplomacy, peacefulness, justice, honesty, indecisiveness, and perfectionism. Ruled by Venus and affiliated with the seventh house.Scorpio: ♏︎ A fixed Water sign. Associated with passion, resourcefulness, willpower, obsessiveness, and manipulativeness. Ruled by Pluto (or Mars) and affiliated with the eighth house.Sagittarius: ♐︎ A mutable Fire sign. Associated with optimism, independence, and impatience. Ruled by Jupiter and affiliated with the ninth house.Capricorn: ♑︎ A cardinal Earth sign. Associated with dominance, perseverance, ambition, resourcefulness, and conceit. Ruled by Saturn and affiliated with the tenth house.Aquarius: ♒︎ A fixed Air sign. Associated with cleverness, inventiveness, wit, independence, empathy, rebelliousness, and aloofness. Ruled by Uranus (or Saturn) and affiliated with the eleventh house.Pisces: ♓︎ A mutable Water sign. Associated with compassion, devotion, adaptability, imagination, sensitivity, and laziness. Ruled by Neptune (or Jupiter) and affiliated with the twelfth house.
Yin-Yang: A Taoist symbol that represents a Chinese philosophical concept, that being the synthesis of dualities. Light and dark, masculine and feminine, active and passive, day and night, winter and summer, order and chaos, etc. are all inherently complementary and part of the same whole, rather than being diametrically opposed. Both Yin and Yang are present in all things.
These are all the most recognizable ones, but individual cultures will also have their own "alphabets" of magical symbols that represent spells or spirits — Icelandic staves, Greek charakteres, and Vodou veves, for example. Then of course there's also the modern practice of making sigils, which are unique designs representing individual intentions, entities, and ideas. There's also an entire directory's worth of alchemical symbols for substances and processes, and that's without even touching on alchemical symbols. Honestly, we could be here all day! But hopefully this was a thorough enough introduction.