Welcome to SolidWorks forums Ivan.
As per SolidWorks KB solution id S-052620, try following:
Please verify permissions to the specific registry key specified in the error message. The easiest way to verify permissions is to:
1) Open the Windows® registry (Start, Run, regedit for XP. For Windows® 7 or Vista®, type “regedit” in the search box)
2) Locate the key mentioned in the error message
4) Right mouse button click on the key and choose “Permissions…”
5) Press the “advanced” button
6) Click on the “Effective Permissions” tab then press “Select...”
7) In box, enter the name used to log into the machine and press “Check Names”, after this press OK
8) Review the effective permissions for the user name; Full Control is required for the SolidWorks installation.
If the above doesn't help then disable UAC under control panel and try installing again.
You might also find this post helpful for your future reference.
Thank you for your answer.
I followed your instructions. When I come to step 6 and click on "Effective Permissions" tab the only message written there is "You do not have permission to view or edit this object's permission settings.". There is no "Select..." button.
What can I do?