Try downloading the zip or 7zip version as you may be having issues with an exe file from a firewall or some security application you have installed preventing the exe file from being saved or opened for reading etc.
Are you logged in as an administrator or simply an ordinary user on your PC?
After a successful archive version download, extract the xampp folder (or drag the xampp folder from the open archive) to your C: drive root so you end up with C:\xampp
Then double click or right click and select to run as administrator the setup_xampp.bat file found in the xampp folder to have the correct paths set in the XAMPP configuration files.
I prefer this method to what is, for some, a troublesome installer exe version anyway.
For what to do next please read the readme_en.txt file also found in the xampp folder.