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Thunderbird does not have a block option that can be used from the menu or toolbar, but it can be made to dispose of unwanted mails using message filters.
Message filters operate on a per account basis, so it is important when you first set up the filter to set it to act on the correct account. The easiest way to do this is select a message from a sender you wish to block and choose Create a filter from message from the message menu. This will open the filter settings windows with the email address already inserted into the filter. Name the filter. My preferred name is "block list". Simply change the action in the bottom half of the window to delete and you are all done. Save the filter and next time that person sends you mail it will be deleted.
Message filter that you have created can be opened and edited by selecting the message filters entry on the Tools menu. It is not necessary to create an individual filter for each address you want to block.
Now you have the block list filter, next time you want to block someone you can add their address into the top of the filter by pressing the plus button and thus creating a new field to enter the new address to be deleted.