I deleted Ubuntu Software Center and I would like to install the software manager instead of Linux Mint.
You will need to have the latest version of Python installed as this is what actually runs Software Manager then in Synaptic Program Manager look for Software Manager or Software Center and tick for installing an next reboot then apply then submit then reboot and when the system reboots the system should start downloading Software Manager and install it and then you should be able to find it in the start menu.