"How can I keep my Outlook contacts in sync with Gmail contacts?"
If you want to sync Outlook contacts with Gmail contacts, there are two ways you can do it. You can do it the hard way, where you export your contacts from Outlook and then import them into Gmail. Or you can sync Outlook contacts the easy way by using software to keep the two contact lists automatically up-to-date.
CompanionLink is the software I recommend to sync Outlook contacts with Gmail. To get the job done the first thing you need to do is download CompanionLink and install it on your computer running Outlook.
After you install CompanionLink, you add your Gmail sign in info to the application, choose how often you want to synchronize your contacts, and CompanionLink does all the work to keep things synchronized. In addition to Contacts, you can also sync your Outlook Calendar with Google Calendar, as well as being able to sync scheduled Tasks from Outlook.

When you order CompanionLink for Google Calendar, be sure to enter LU3300 in the Affinity Code box.
See also: If you want to import messages from Outlook to Gmail, see this guide on how to add Outlook email to Gmail.
