The game automatically saves
(1) at the start of every turn, you can access this by hitting ESC and choosing "Retry Turn"
(2) at the start of every level, you can access this by hitting ESC and choosing "Retry Level"
(3) before the start of any mission in your safehouse (excluding the first mission), you can access this by hitting ESC and choosing "Abort Mission" << this needs to be renamed.
Then, on the ESC menu there are 4 manual slots with buttons for Overwrite / Load. The game never automatically writes to those, they are only overwritten when you click the UI.