A third party has being used My Apple ID to Purchase apps

You are sure they're genuine emails from Apple and not a phishing attempts trying to get your account and payment details ?

Phishing and similar emails : Avoid phishing emails, fake 'virus' alerts, phony support calls, and other scams - Apple Support

Genuine iTunes emails : Identifying legitimate emails from the iTunes Store - Apple Support

Viewing an account's purchase history : See your purchase history in the iTunes Store - Apple Support

If they are genuine, and if you claim you didn't do them (I assume you've already changed the account's password etc.) contact iTunes Support : http://www.apple.com/support/itunes/ww (click on your country's flag, the country where you live, and which is therefore the country on the account ; click on Contact Support towards the top right ; click on Get Help under 'Talk To Us’)

Apple will always address you by your name or the name they have on file for you, not Dear Customer, Dear Client or by using your e-mail address.  The e-mail will be from @apple.com or @iTunes.com. E-mail addresses can be spoofed. You can go to Mail/View/Message/Show all Headers to see more. Apple e-mails will never contain an attachment. Apple will never request personal information by email such as Social Security numbers, your Mother’s maiden name or full credit card numbers .

The only exception to the above I have noticed is if you order something from the Apple Store (apple.com), your receipt will be addressed to Dear Apple Customer. That is a receipt for a purchase you initiated.