Problem with my Mac

I own a Macbook Air and it's currently having problems. After installing a routine software update, my Mac crashed. It is now stuck on the Apple loading screen with the Apple that starts on on Macs. Help would be appreciated.

You need to provide us with some more info:

Year and model MacBook Air?

Version of OS X it's running?

Which software update did you download and did you make a backup prior to installing the update, or any backup?

It is the mid 2011 11 inch model. It is running OS X Lion. The software update that was downloaded was the standard Software Update that appears in the toolbar. I often installed the update. I didn't make a backup before the update.

OK, thanks for posting back the specs for your MacBook Air.

Normally, software updates are benign and do not cause problems. It may have been coincidental with another problem your MBA was having. Anyway, let's try this:

Boot your MacBook Air to its recovery partition. Reboot and hold down the command plus the r key. The machine should boot to the recovery partition. It may take a few minutes to do so. Once in recovery, choose utilities, and then select Disk Utility. Run verify and repair for the hard drive. Let us know the results.

I was told that my Macintosh HD could not be repaired but it reads another disk called Apple SSD TS064C Media.

Your MacBook Air has an SSD divided into three parts: A small EFI partition, the main Macintosh HD partition, and the partition you booted to called the recovery partition. Disk Utility is telling you that your Macintosh partition can not be repaired. All your data is on the Macintosh partition.

but it reads another disk called Apple SSD TS064C Media.

Click to expand...

That's the SSD which is in your MacBook Air. See above for how it's divided.

So am I unable to fix my Mac?
If not, thank you for all your help.

I didn't say you couldn't fix it, however, it will probably mean replacing the defective SSD. That's why it's very important to make backups. Since your machine is a 2011 model, did you buy extended Apple Care? If you have Apple Care, Apple will replace the SSD.