I cannot open my iPhoto since e I updated my mac?

iPhoto was discontinued 6 years ago. It is no longer developed or sold. It's so old that it no longer runs on recent system software. The good news is that it was replaced by the more powerful (and free) Photos.app that comes with the OS. You can migrate to that app very simply:

Hold down the option (or alt) key and launch Photos. From the resulting menu select 'Choose Library' and point at your iPhoto Library. It will do the rest.

If you prefer not to use Photos there are several 3rd party apps that you can use. Which to choose depends on the kind of photographer you are and your budget.

I have asked the same question on a separate string on the same theme. When you transfer from Iphoto will the Events and Albums folder be maintained. All the advice I have taken (Genius Bar, Helpline), suggests they will not. When you talk about 3rd party apps are you talking about Photoshop, Lightroom?

a: the transition from iPhoto to Photos is non-destructive. So you can safely experiment by doing it yourself and exploring the options. There are differences. Events as a concept is no longer used, and your Events are changed to Albums. I don't believe your Albums are preserved.

b: Photoshop is a pixel editor with no organising capability whatever. Lightroom Classic is very much the industry standard photo manager, a pro level app whereas iPhoto and Photos are definitely at the consumer end of the market. There is another Adobe app, just called Lightroom, which is like a more powerful version of Photos, and web based. These are not the only options. A very good app called Mylio is a higher end consumer app, there are the open source DarkTable and Digicam, as well as apps like On1 Photo Raw and Exposure 7.