The name, quartz, comes from the Greek word, krustallos, which means ice.  It's often referred to as "the ice of the Gods".  Quartz is the most abundant single mineral on earth and makes up about 12% of the earth's crust because it occurs in a wide variety of igneous, metamorphic and sedimentary rocks.
Quartz is the chameleon of gemstones, often standing in for more expensive gemstones from diamonds to jade but is now starting to be appreciated for its own attributes.   Quartz comes in many different varieties including Amethyst, Citrine, Rock Crystal and others.  The most common color is clear but the colors range from clear to milky white to pink, purple, gray, brown and even black.  Cryptocrystalline varieties are sometimes multicolored.  Varieties are divided more by character than by color, however.

Amethyst
Amethyst is a variety of quartz and varies in color from pale lavender to a deep, rich purple.  Amethyst has a hardness value of 6.5 to 7.0.
Some people believe amethyst can be used to remove undesirable attributes in the soul and bring about a more intense spirituality.  It is said to deflect and redirect energies instead of absorbing them.  Users of this powerful crystal believe that amethyst operates on levels that are out of our normal range of senses.
Amethyst has been often given away as a symbol of sincerity.  It is said to lend a feeling of security and contentment.

Citrine
The word "citrine" comes from an old French word, citrin, meaning yellow.   Citrine is a quartz crystal, which varies in color from pale yellow to deep amber.
Citrine has a hardness value of  7 and is often used as a substitute for the birthstone for November.  It has also been designated the gemstone for thirteenth wedding anniversaries.  The astrological signs of citrine are Gemini, Aries, Libra and Leo.
Citrine's metaphysical properties are thought to include stimulating one's mental capacities, enhancing creativity and intuition and bolstering self-confidence.  It is believed to inspire warmth, prosperity and ease.  It's further thought to help self-realization and personal goals to work together in harmony.  According to legend, citrine protects against snake venom and evil thoughts.

Rose Quartz
Rose quartz varies in color from peach to pink and it is, of course, part of the quartz family.
Rose quartz has a hardness value of 7.
Most rose quartz is dyed to achieve the desired color, though there are some natural occurrences.
Rose quartz is know as The Heart Stone, and is said to balance emotions and open the heart.  It is believed to foster the joy of life and happiness and bring about contentment in love.  Some believe it fills one with optimism, tenderness and gentleness.
In addition to helping with romantic love, rose quartz is believed to enhance all other forms of love as well, including self-love, platonic and maternal forms of love.   It's said to "emanate unconditional love" and is supposed to help us attract positive aspects of love into our lives.
Rose quartz is probably one of the most prized stones for it mystical properties.   Sleeping with it under your pillow is supposed to help you release the pain of the past through your dreams.  It's supposed to help heal the child inside us all.   It's believed to bring about a feeling of self worth and self-empowerment.   People believe it can be of great help and comfort to brokenhearted people who have recently lost a lover.

RUTILATED QUARTZ
Rutilated quartz is identified as quartz crystal containing rutile crystals growing within it.  The chemical composition of rutile is titanium dioxide and occurs as "hairs" or thin, straight crystals with a metallic luster.  It has a hardness of 7.  Rutilated quartz is said to intensify the power of the quartz crystal.  It is said to bring strength and tranquility with love, and ease transition and growth with reason and order.  It is used for healing and balancing the aura and stabilizing energy.

SMOKY QUARTZ
Smoky quartz has a hardness of 7 and can be gray to warm brown, light and almost clear to an almost "solid" looking black/brown.  The coloration is due to natural radiation occurring in its environment.
Smoky quartz is said to dissipate negativity and balance energies of mind and body.   Good for meditation, it also enhances dream awareness and channeling ability.   Some folks claim it is a protective and grounding stone.  Others say it aids in fighting depression, is mildly sedative and relaxing.