A birthstone is a gift of a precious material (jewelry, mainly gemstones; themselves traditionally associated with various qualities) that symbolizes the month of birth (in the Gregorian Calendar).

It is sometimes also called birthday stone (cf. infra; but that word is, confusingly, sometimes used as a synonym for an anniversary gift, which is related to the recipient's age, i.e. year of birth).

There have been many different sets of birthstones used throughout history and in different cultures, but in 1912 the American national association of jewelers, Jewelers of America, officially adopted the following list; it is currently the most widely used list in the United States and many other places, including Australia (a jeweler's 'modern' list states they are selected for bright colors) and Thailand:
January: garnet
February: amethyst
March: aquamarine or bloodstone
April: diamond
May: emerald
June: pearl (the only non-gem) or moonstone or alexandrite
July: ruby
August: peridot or sardonyx and sapphire
September: sapphire
October: opal or tourmaline
November: topaz (apparently not in blue, cf. infra)
December: turquoise or lapis lazuli (the blue stone in pharaonic jewelry) or zircon or blue topaz Tanzanite was added to December by the American Gem Trade Association in 2002.

Zodiac stones

This is an astrological version of the birthstones, using zodiac signs in stead of calendar months of birth, and one completely different stone.
Aries (March 21 - April 20) Diamond
Taurus (April 20 - May 21) Sapphire
Gemini (May 21 - June 20) Spinel
Cancer (June 21 - July 22) Emerald
Leo (July 23 - August 22) Ruby
Virgo (August 23 - September 22) Opal
Libra (September 23 - October 23) Peridot
Scorpio (October 24 - November 21) Aquamarine
Sagittarius (November 22 - December 21) Topaz
Capricorn (December 22 - January 21) Garnet
Aquarius (January 20 - February 18) Amethyst and moonstone
Pisces (February 19 - March 20) Diamond

Birthday stones

While this word has also been used as synonym of Birth stone (see above), there is a separate list of assignment according to the day of the week of the recipient's birth:
Monday : Pearl (again the only non-gem)
Tuesday : Garnet
Wednesday : Cat's eye (Chatoyant Chrysoberyl)
Thursday : Emerald
Friday : Topaz
Saturday : Sapphire
Sunday : Ruby