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The Grid Geometry Manager
The Grid geometry manager puts the widgets in a 2-dimensional table. The master widget is split into a number of rows and columns, and each "cell" in the resulting table can hold a widget.
The grid manager is the most flexible of the geometry managers in Tkinter. If you don't want to learn how and when to use all three managers, you should at least make sure to learn this one.
The grid manager is especially convenient to use when designing dialog boxes. If you're using the packer for that purpose today, you'll be surprised how much easier it is to use the grid manager instead. Instead of using lots of extra frames to get the packing to work, you can in most cases simply pour all the widgets into a single container widget (I tend to use two; one for the dialog body, and one for the button box at the bottom), and use the grid manager to get them all where you want them.
Consider the following example:
Creating this layout using the pack manager is possible, but it takes a number of extra frame widgets, and a lot of work to make things look good. If you use the grid manager instead, you only need one call per widget to get everything laid out properly (see next section for the code needed to create this layout).