Gmail has a dedicated Filter tool that customizes what action to take on messages people send to you. You can use the Filter tool to redirect messages from an email address directly into your trash, blocking all messages from the address from ever appearing in your inbox. The sender is not notified when you block him.
Enter the email address you want to block in the Search field at the top of the screen.
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Click the arrow at the end of the Search field.
Enter the email address in the From field if it's not there already. The email address may show up in the "Has the words" field first.
Click the Create filter with the search link in the bottom corner of the expanded search filtering dialog.
Place a check mark in the Delete It check box.
Click the Create Filter button to confirm you want to immediately delete all emails that arrive from this sender.
You can also block an email address by creating a filter based on an existing message, rather than searching for an email address. Place a check mark in the check box next to a message from the person or people you want to block. You can select multiple senders simultaneously. Once you’ve selected the person or people you want to block, click the “More” button, choose “Filter messages like these,” check the "Delete it" check box and click "Create Filter."
To edit an email address you’ve blocked, or to remove the blocking altogether, click the “Gear” icon in the top corner of Gmail and select “Settings.” Click the “Filters” tab and locate the filter you set up to block the email address. Click “Delete” to unblock the email address. Click “Edit” to change the address or how it’s filtered. Make your changes, click “Continue” and then click “Update Filter.”
If you have more than one Gmail account, you can transfer filters from one to another to block users without having to manually create blocking filters in each of your accounts. Click the “Gear” icon and choose “Settings.” Click the “Filters” tab, select the filter or filters you want to export and click “Export.” Save the exported file, open your other Gmail account and this time select “Import” on the filters tab to import your filters.