Most of what you find in Sharia law is custom and tradition. Some of the meanings are widely disputed by different factions of muslim world. The interpretation of the Koran is similar to the interpretation of the bible with widely differing belief sets.
Most of the Muslim world does not implement the severe punishments often quoted.
Radical beliefs attempt to interpret the Koran in literal ways, while more moderate Muslims attempt to base interpretation of Sharia law with reason and common agreement. For example, Christian beliefs regarding such things as 'an eye for an eye' are generally interpreted to mean that it is not nice to hurt someone else. The more radical belief could be that revenge is necessary and right.