So I bought minecraft today, and played a game with my friend which was fun. But It's on his world, and when he quits the game, I can no longer play the game.

If I wanted to do this on my own, is there an option to have a multi player map? Like a shared one, that anyone can play when they want? Is it possible? If so, can you talk me through how to create a new multi player world from the home screen? Also, if it's possible to change a map into a multi player map, can you talk me through how to do this as well? Thanks in advance.

Also. If MOJANG ARE READING THIS, Please make it so that you can play the multiplayer map without the host needing to be playing on the same map at the same time)