Deleting E-mails from Inbox From One Sender

1. Open one of the messages.
2. Find the "More" button (there are two, you want the one just over the message, not the one above it on the toolbar.
3. From the More menu, select "Filter messages like these".
4. If the filter is OK, then click create filter.
5. Click delete
6. Select the "apply filter to ____ messages like this".

This will continue deleting any similar message that comes in the future.

I suspect that's just what you will have to do. That is, check each one and then delete all the checked mail at one time.

Now, in Yahoo Mail, instead of deleting them all, you can also report one or all as spam. Yahoo will block that address and you'll never see them again. I imagine gmail has the same potential, I've just never done it there.

If you had answered 2 minutes sooner, I wouldn't have bothered. Yours is better, but you never know which questions are going to be answered.

Can I delete all the old e-mails with this filter, without blocking the new ones that will arrive each week?

You can type in the Search box "from:(sender email address)" then check the box of the mails you want to delete -> delete them as normal.
Filter tool may make all the incoming mail be deleted, so hope this help you somehow.
The result may include all the email in Sent Items, Draff Box.