Mac OS X Mavericks Contacts Database is a SQLite db, how can i open it with a SQLite App? i have an Sqlite Browser App.
I would like to view and extract all Contacts of the Contacts App for further use in a FileMaker Pro file ... 
How can i connect to this database and export its content ?
Address Book contacts and data are stored in 

~/Library/Application Support/AddressBook/AddressBook-v22.abcddb.  

You will have to load the file into your Sqlite Broswer App and export whichever tables you want.  Each field in a contact is set to a different table. 

While in the Contacts.app do a File-->Export.  This is a good idea to make a backup of your contacts before you start playing with the database it uses.  Not knowing what sqlite app you use it's hard to say but there should be an option to Export whatever tables you need.