The classic theory that all things within the entirety of the known Universe are made of basic building materials and can be categorized.
The Three Element System
The three fold system contains the classical elements of Fire, Water and Air, as well as the Alchemical elements of Sulfur, Salt and Mercury. It is symbolized, referenced, and contained in the Tarot, Sepher Yetzirah, and the Rose Cross. Its pattern can be seen in material science as proton, neutron and electron as well as the Christian trinity and in the Triple Goddess traditions. This Universal system symbolizes the Universe as a triangle consisting of a Masculine (Fire/Sulfur), a Feminine (Water/Salt), and an Androgynous harmonizer (Air/Mercury).
Fire is Masculine and; in Hebrew Kabbalah it is Shin, it is the Judgment Tarot card, in Alchemy it is Sulfur, in the Greek IAO it is A for Alpha and is the Father in Christian trinity.
Water is Feminine and; in Hebrew Kabbalah it is Mem, it is the Hanged Man Tarot card, in Alchemy it is salt, in the Greek IAO it is O for Omega and it is the Son in Christian trinity.
Air is androgynous and; in Hebrew Kabbalah it is Aleph, it is the Fool Tarot card, in Alchemy it is mercury, in the Greek IAO it is I for Iota and it is the Holy Ghost in Christian trinity.
The Four Element System
Evolving from the three element system came the four element system, which beget the fourth element Earth. Earth is the product of a combination of the prior three elements. Like the three element system, the four element system has an Hermetic Qabalah equivalent in IHVH commonly referred to as the Tetragrammaton. There are more than a few esoteric methods to order the four elements; by cardinal direction, the magical weapons and Kerubs of the Tarot, by the IHVH system of the Hermetic Qabalah, the Neo-Enochian system of the Golden Dawn, and the hexagram method of alchemy.
Cardinal direction: North/Earth, East/Air, South/Fire, and West/Water.
IHVH: Yod/Fire, Heh/Water, Vav/Air, and Heh/Earth.
Waite Tarot and Golden Dawn Enochian:
In the Waite Tarot the four elements ascribe to the four magical weapons pictured in the Magician card. Also, in the Waite Tarot the four Kerubs pictured in the 10th card Wheel of Fortune and the 21st card The World represent the four elements as the creatures of the fixed zodiacal signs: Air/Aquarius/Man, Fire/Leo/Lion, Water/Scorpio/Eagle, and Earth/Taurus/Bull. The Kerubs can be found in the corners of each card and are located in the slots allocated by the Golden Dawn's Enochian Watchtower Tablets; Upper Left/Air, Upper Right/Water, Lower Right/Fire, and Lower Left Earth.
Hexagram method of Alchemy; The hexagram method of alchemy places the masculine elements of Fire and Air, over the feminine elements of Water and Earth represented by triangles. The mother and father elements of Water and Fire are given an inverted triangle and an upright triangle respectively. The son and daughter elements of Air and Earth are given their respectively aligned triangles with a horizontal line through them to represent the intersecting opposite triangle on the hexagram.
The Five Element System
The most common elemental system in use today is the five elemental system because of its association with the popular symbol of the pentagram. The pentagram represents the four classic elements crowned or ruled by the fifth element of Spirit. The Golden Dawn again ascribed the placement of the elements on the pentagram congruent to their Neo-Enochian Watchtower tablets.
Plato used this system and ascribed solids to represent each element. Plato reckoned that these tiny solids of the elements made up all things within the Universe, and although Plato is wrong by modern scientific standards, his observation opened up the world of molecular composition.
The Five element system also has ascribed to it an Hermetic/Christian Qabalah word of power known as the Pentagrammaton. The Pentagrammaton, like the Tetragrammaton, contains the four elements but with the addition of spirit which is located within the heart of the word. The Pentagrammaton also has two spellings, one which represents spirit as the reconciling element between the upper and lower worlds and one with spirit among us within the lower worlds. IHShVH or Jeshuah represents spirit as the Reconciler and this is spelled; Yod/Fire, Heh/Water, Shin/Spirit, Vav/Air and Heh/Earth. IHVShH or Jehovasha represents spirit among us and is spelled; Yod, Heh, Vav, Shin, Heh.
What's in it for me?
It is this author's opinion that the elemental systems show an evolution of thought and philosophy. The three elemental system is the most ancient system and one of materialization and could be described then as maternal. This can be seen in matriarchal cults and traditions in their rules of three and three headed goddesses. Therefore, using a three elemental system would be ideal for divination, evocation and conjuring.
The four elemental system appears to be the next step from the three tiered system. It places masculine over the feminine and can be described as patriarchal. The square of the four tiered system is stable and mathematical and therefore is ideal in talisman making, sigil craft and anything which uses encryption and words of power.
The five elemental system is the current system used by most modern mystery schools and traditions. It is androgynous and places importance not in one type of element whether active or passive, male or female, but places an emphasis on a reconciling middle path which makes use of both of the above mentioned systems. Therefore, using a five elemental system would be ideal for any and all operations as it contains both a three and four elemental system. After all a pentagram is the sum of the triangle and the square transposed one on top of the the other.
At the end of all things we can realize that the three, four, and five systems are actually three in number and reflect once again a masculine, feminine and androgynous quality respective to each. This is one example of why the elemental structure is universal, fractal, and even unending. The elemental systems have a home in the global unconscious and conscious of the human race as well as the universal conscious itself, which is why the elements remain a mainstay of modern practitioners of the Western Mysteries to this day.