Q: Since updating my macbook pro I have no memory left. Help!

Are you saying that your storage is full?  If so, try a Safe boot and if successful, transfer items to an external drive and delete them from the internal HDD.  DO NOT FORGET TO EMPTY TRASH!

http://support.apple.com/kb/HT1564

It would be helpful if you indicated the EXACT MBP that you have.

Ciao.

What is a safe boot and how do I do it?

Click on the link Ogelthorpe gave you.

If the Safe Boot fails to give you access yo your MBP, you will then have to try Target Disk Mode with another Mac:

http://support.apple.com/kb/HT1661

Or take out the internal HDD, install it in an enclosure and connect it to another Mac.

Again, it would be helpful if you indicated the EXACT MBP that you have.

Ciao.

Target Disk mode is not a backup, but by connecting in Target mode you may be able to make a backup.

It may very well be your mailbox that is the problem, but you have to access the HDD in order to clear out data.  That will have no affect on your ability to use your e-mail application with your MBP.

Try the three suggested options for accessing your MBP HDD.

Ciao.

HDD = Hard Disk Drive.  That is where all of your data is stored in your MBP. 

Ciao.

I had the same model and it had one problem after another. I bought it in September last year and in less than a year, Apple already replaced, three logic boards, two hard drives, hard drive cable, hard drive bracket, graphics card, and graphics card. After the second hard drive failed in June, Apple finally decided to replace it and so I upgraded to a 13" retina.