From-> Mac OS X 10.5.8 (9L30) To-> OS X Mountain Lion

https://discussions.apple.com/thread/4375496

You can't upgrade in the sense of installing ML over the top of Leopard, but you can wipe your internal disk and install ML as a fresh OS, so long as your computer meets the system requirements. See my post here for a list of supported machines and a link to the tech specs.

http://applehelpwriter.wordpress.com/2012/08/03/will-mountain-lion-work-on-my-ol d-mac/

If you meet the requirements, the next step is to get hold of the ML installer. Before thinking about that, make a clone of your current OS on an external disk for safe-keeping in case anything goes wrong. Use Carbon Copy Cloner to do that.

The easiest option to get the installer might be to contact your nearest Apple store and see if they will install it for you. If they won't, the only other way I can think of is to log into the App store using your AppleID from another Mac (perhaps a friends'?) that is running 10.6.8 or later, and to download the installer and save it to disk. You'd then need to make a USB or DVD installer from that, by following the instructions here:

http://arstechnica.com/apple/2012/07/how-to-create-a-bootable-backup-mountain-li on-install-disk/

Take the installer back to your own mac, boot from it, wipe your internal OS (remember: make a backup clone before doing this) and click 'Install'.

(ToU Disclaimer: links to my website contain other links which promote my services as a technical writer)

Call Apple to buy Snow Leopard. Make a backup, insert the DVD and upgrade. Finally, open  > Software Update and install the latest version

It will cost $29

Open > http://support.apple.com/kb/HE57

deleted by Softwater (unnecessary post)