Will a Steam account work across platforms?

Solution 1:

The same Steam account will work on all platforms. Most games don't work on both Mac and Windows, though, so bear that in mind. You can find out the compatible platforms for each game on their Store page, at the bottom with system requirements. Steam should still always let you buy any game (available in your region) for any platform.

Solution 2:

Yes, you can !
You will be able to connect to steam even from your phone, but some games may not work for mac and some may not work for pc, but you can still buy games for windows from a mac and games for mac from windows.