*.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.