*.exe files are a Windows/DOS thing. They will not run natively in Linux.
You can run some *.exe files using
WINE. The
Wine AppDB provides some information as to what applications run well with WINE and what ones do not, at least as regards major applications.
Another alternative is to install a virtualizer, such as VirtualBox, install Windows to the virtualizer (that is called a "virtual machine" or VM), then run the files in Windows in the VM. This article should tell you more:
https://help.ubuntu.com/community/VirtualMachines
Between the two choices, I would recommend the latter over the former. When WINE works well, it's great, but, depending on the file you want to open, it may or may not work.