Mosaic Laws are categorized into 613 mitzvot.
A list as well as an overview of how to get to this number can be found at http://www.answers.com/topic/613-mitzvot-1
The Laws are commonly called the "Mosaic laws" because it is traditionally believed that they were written down by Moses.
613
There are lots of them, in almost all the five books. There are 613 laws.
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All of them. They are not laws until the ruling body accepts them as such, by whatever means is used by the country concerned.