The birthstones come in several sets and the list of the stones can therefore vary between different cultures and countries. 

Here's our list:

January = garnet ( also rose quartz )
February = amethyst ( also onyx )
Mars = aquamarine ( also heliotrope and jasper )
April = diamond ( also rock crystal )
May = emerald ( also chrysoprase )
June= moonstone and pearl
July = ruby ( also carnelian )
Augusti= peridot ( also aventurine )
September = sapphire ( also lapis lazuli )
October = opal and tourmaline
November= yellow topaz (also citrine and tiger's eye)
December= turquoise ( also zircon, blue topaz and tanzanite )

The starting point for our list has been the book Gems and Ornamental Stones by Walter Schumann, Second Edition. We have then added new stones and adjustments.