carlosrafa :
I bought my notebook in 2008
I glossed over the other part of your question.
Will this improve the performance of my notebook?
To some degree it will. Applications and OS will load faster. You are still limited by a very slow CPU and likely very little RAM.
I've got one or two Core 2 Duo. While an SSD will make them feel more responsive. They still get bogged down easily. Even some web pages are very slow. The CPU simply isn't fast enough. Just a couple web pages can overload them. That's with a Core 2 Duo around 3Ghz.
I've looked up your laptop. It uses at best what was a low end Core 2 Duo at the time. It also only uses SATA I. It doesn't matter what you do. That computer is old and slow.
If you are asking if you should upgrade. No, you should not. You can easily pick up a used 3rd or 4th gen i5 laptop with an SSD, Windows 10 and 8GB RAM for under $150 on eBay from a US Seller. You can get a 1st gen i5 with SSD and 4GB RAM for under $100. Either would be a monumental improvement.
Although I'd try to get a newer 3rd/4th gen. As they have much more recent tech improvements in the CPU. They'll support SATA III, possibly USB 3.0 and some may support 802.11ac. They'll also likely have larger trackpads.
Just pick a good seller and read the description carefully.