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In Access 2013, in the External Data tab, you'll see a section called Import and Link. Select the "More" drop-down menu then select "Outlook Folder". From there, you can link an Access database (I started from a blank database) to Outlook 2013 and you'll see all of the contacts from Outlook in the Access database now.
Based on my tests though, changes don't sync both ways; they only sync from Outlook 2013 to Access 2013, so you'll have to make all of your changes through Outlook 2013, and then click the "Refresh" button on the "Home" tab in Access. The data does refresh and you don't have to re-import anything, but it only goes one way, that I could find.