How to open Logitech MX Air mouse to replace battery

Look at the mouse from the back side . First, make sure the mouse is shut off. There are 2 small short screws near the top and two small longer screws near the contacts at the bottom. Remove all 4 screws ( I needed a #0 Phillips screwdriver). Carefully open the two halves being careful not to stretch the wires too much. Without disconnecting any cables, slide the larger ribbon cable out from it's retainer. It should come out easily, but don't put stress on it. This will allow you to get the back further out of the way. Then see 4 larger short screws holding the front on (I needed a #1 Phillips screwdriver). These screws are all near the battery. This separates the front, but you have to lift the front at the bottom and slide it down to get it open. Once that's open you will see the battery. It is not secured with screws, but can be dropped out. Notice that there are 3 contacts on the battery, so insert the new battery so the contacts meet the spring contacts that are part of the mouse. Carefully slide the front back on towards the top. It can be a little tricky to get it lined up properly. Once that's slid in from the bottom you can press the bottom of the front in place. Then reinsert the 4 larger screws to secure the front, replace the ribbon cable under its retainer and replace the back. Finally replace the 4 small screws and put the mouse in its charger. If you did everything correctly the mouse should start to charge.