I just bought Outlook 2013 and the sent email is not saving in the sent folder.  I'm a paperless company and MUST be able to track my sent emails.  Where are they??  I can't believe I paid for Outlook when it has such a huge flaw. 

They should end up in the sent items folder. What kind of mailbox are you connected to? Exchange, POP3 or IMAP? Do you just have a single mailbox configured or do you have more than one?

If you go into File, Options, Mail, and then scroll down to the Save Messages section (6th section down), is "Save copies of messages in the Sent Items folder" checked? If not then it should be.

It's IMAP.  The "Save copies of messages" is checked.  Please answer my question:  Where are the emails I sent before I discovered that each individual sent message must be saved?  Are there copies somewhere on my computer?

Also, I have checked the delivery and read receipts on all of my sent emails, as I must have these confirmations for my business, and I get nothing.  Where are they?  all the right boxes are checked.

depending on your setup, and, how you choose to manage your emails (e.g. filing incoming messages into different folders), this article may help:
http://office.microsoft.com/en-au/outlook-help/outlook-2013-replies-arent-saved-to-the-originating-folder-HA104041411.aspx?CTT=1

also, since your question is specific to Outlook, you may find further specialised assistance in the dedicated Outlook forum (where Outlook MVPs hang out)

http://social.technet.microsoft.com/Forums/en-US/home?forum=outlook

there are some similar discussions at the MS Answers forum:
http://answers.microsoft.com/en-us/office/forum/office_2013_release-outlook/outlook-2013-is-not-saving-my-emails-that-i-send/57ae2c25-0c7c-427b-80f8-279aac84b970

You didn't answer the question--and the article was equally unhelpful.  I've posted in the "Outlook Forum" but doubt I'll get any help there.  What a waste of money