Scroll through open dialogue with the user down and find the button "Hide conversation". After clicking it the dialog will disappear and no longer trouble you with my presence.
You can delete correspondence with the user completely. For once you can only delete one conversation with a specific person. To do this from the main page of the social network go to "Messages" then you will see a list of all conversations with contacts.
Locate the desired correspondence using the search bar and hammering it the name of the person. If you have a small number of conversations simply scroll down the page. Click on friend's photos. In the history messages click on the "Delete all messages" at the top. In the future, to begin a new dialogue with this person, you will need to go to its page and select "Send message".
You can delete the entire conversation, but only some of its messages. Click on one of them, which you don't need and select "Delete message". Confirm your actions by replying positively to a dialog box.
If you want, you can restrict receiving messages from other users by setting appropriate privacy settings. Your profile will open and you will be able to send messages to those who are present in your contacts list. For other users this feature is available only if you approve their request for a friend. Go to "More" located under your photo. Click on it with the left mouse button and select "Edit settings". Go to line "Options of publicity." Select the option "text me". Specify the option "Allow only friends".