There are far too many pane operations, so we'll not be able to cover all of them exhaustively in this book; for most that we'll not discuss, we implore you to dig into the tmux man page:
$ man tmux
Alternatively, you can refer to them on the Web at http://man.cx/tmux.
Now that you understand panes, the man page should be very manageable and understandable on the topic of panes.
You can do things like breaking one pane out into its own window; rotating the panes; swapping one pane with another; moving a pane to another window; and arranging all the panes horizontally, vertically, tiled, and much more.
There are many more commands to resize panes, many of which don't even have keyboard shortcuts because they're not used all that much. Of course, you could add your own, and if you read Chapter 2, Configuring tmux, you should have all the tools in your toolbox to do so.