Invitations to connect can be sent to anyone you have an email address for (LinkedIn member or otherwise). Once they accept your invitation to connect, you can message them directly through LinkedIn. Learn more about invitations.

InMail messages are private messages that allow you to directly contact any LinkedIn user, while protecting the recipient's privacy. Learn more about InMail.

Messages can be sent to your 1st-degree connections from the LinkedIn messaging page, your Contacts page, or their profile page. Learn more about sending messages.

You can use the Open Profile feature to contact Premium members for free.