Minecraft: continue playing the same map on mobile phone and PC?

Have a map on PC but would also like to play on mobile phone from time to time. Can I take turns playing, so have the same map and when I have made progress, will it be saved for both?

It depends on the version. If you play the Java version on your PC, you can't play it on your mobile phone. But if you play the Windows 10 version (Bedrock) you can. Then you have to copy the map. You can find tutorials on YouTube under search terms like "Copy Minecraft Bedrock World" or something.