Adamite
Location: Mexico
Chemical Composition: Zn2AsO4(OH), Zinc Arsenate Hydroxide
Hardness is 3.5

Agate 
Alternate birthstone for May
Location: Mexico
Variety of: Chalcedony
Chemical Composition: SiO2 silicon dioxide 
Hardness: 6.5 to 7
 

Ajoite in Quartz
Location: Messina Mine
Messina, S. Africa
Quartz with turquoise colored inclusions.
Chemical Composition: (K, Na)Cu7Al(Si3O8) 3(OH)6 - 3H2O, Hydrated Potassium Sodium Copper Aluminum Silicate Hydroxide
Hardness is 3.5

Alexandrite
Location: Russia
Variety of: Chrysoberyl
Chemical Composition: BeAl2O4 + Fe,Ti beryllium aluminum oxide
Hardness: 8.5
 

Amazonite with smoky quartz
Location: Lake George Area Colorado, USA
Chemical Composition: KAlSi3O8
Hardness: 6 to 6.5

Amber
Location: Baltic
Organic Gemstone
Amber comes translucent or opaque, with colors ranging from milky to red, brown, gold or even black, blue, or green
Chemical Composition: Approximately C10H16O; Succinic acid
Hardness: 2 - 4 Very soft, easy to carve or melt
 

Amethyst
Birthstone for February
Location: Bolivia
Light to medium delicate purple to lavender.
Variety of: Quartz
Chemical Composition: SiO2 silicon dioxide
Hardness: 7

Apache Tears
Location: Arizona
Chemical Composition: Volcanic, amorphous, siliceous glassy rock
Hardness: 5 - 5.5

Aquamarine
Birthstone for March 
Location: Brazil
Variety of: Beryl
Chemical Composition: Be3 Al2 Si6 O18
Hardness: 7.5 - 8 
 

Atacamite
Location: Chile
Chemical Composition: Cu2Cl(OH)3, Copper Chloride Hydroxide
Hardness is 3 - 3.5

Azurite Nodules
Location: Mexico
Chemical Composition: Cu3(CO3)2(OH)2, Copper Carbonate Hydroxide
Hardness is 3.5-4

Barite
Location: Romania
Vitreous resinous colorless, blue, white, yellow, brown, gray. etc.
Chemical Composition: BaSO4, Barium Sulfate
Hardness is 3 - 3.5

Bloodstone
Alternate March birthstone
Location: India
Variety of: Chalcedony
Chemical Composition: SiO2 with impurities
Hardness: 7