This is a basic guide on using the Inkscape Path Operations. After writing a lot of intermediate tutorials on creating vector art, I found that I extensively use the path operations. Many questions were asked on how one can get a specific shape in other tutorials, and the answer would be obvious if you have a in depth understanding of these operations.
Path operations are performed between two shapes. All the path operations can be found in the Path menu. Depending on the order of the shapes, and the operation performed, you can get various derived shapes. The different operations we will look at in depth are the following.
 Union
 Difference
 Intersection
 Exclusion
 Division
 Cut Path
I use the Union, Difference and Intersection a lot, and the knowledge of these three operations should be sufficient for most of what you want to get. For completeness, I will discuss the other three operations too. To apply all these operations, you select two shapes, and then choose the operation required from the Path menu.
Union
Hot key: [Ctrl] + [+]
It combines two shapes into one shape. Even if the two shapes are not overlapping, it makes it into a single path object. You can use it in vector illustrations, when you create it part wise, and then want to combine them to give uniform effects like gradients.
Difference
Hot key: [Ctrl] + []
The Difference operation punches out one shape from the other. The one that is on the top is used as the stencil to cut out the shape from the lower shape. Observe how the same operation is performed on the above shapes, when their order is swapped.
You can use this operations to punch out shapes from larger shapes to give them details. Note that for this operation to take effect the shapes must be overlapping.
Intersection
Hot key: [Ctrl] + [*]
The third of the most used operation, the Intersection operation chops off any part of the shapes that are not overlapping each other. Use this operation to put in shapes of shadows that follow the exact boundary of the original shape, by intersecting the shadow shape with a copy of the original shape.
Exclusion
Hot key: [Ctrl] + [^]
This operation result is opposite to that of the Intersection operation.
Division
Hot key: [Ctrl] + [/]
This operation breaks the lower shape into two shapes based on the overlapping shape.
Note that the order of the shapes overlapping each other effects which shape is broken into two.
Cut Path
Hot key: [Ctrl] + [Alt] + [/]
The Cut Path operation is similar to the Division operation, except that the resulting paths are kept open and not close – making the fill color in consequential.
Like the Division operation, the order of the shapes effects the result.
I have not yet found much use for the last three operations. For the first three operations, I can give practical examples of why I would use it. But if you do know of any practical use of the last three Path Operations, do let me know.
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Nice compilation of the path operations. These operations are so basic, I took some time to learn them myself. It is really helpful for starters.
I have an application for path division in my tutorial on designing a diamond here. 
nice!
Could you show how to make blurred “shadow” to cut with intersection, so that result is “inner shadow” ?

Thanks for your help!!

Thanks this was useful. The fact that you don’t use the last three functions probably means that there’s another way of doing what I did. I used the division function to split a shape and then have different fills in each part.

How would I get “division” to split open more than 1 object?
If I have 2 boxes… I “group” them as 1 object.
Then I try to “split” them with “division” by a 3rd object and it does nothing.
What am I doing wrong?

You can’t punch a group of shapes out of another with none of the settings; I worked out that by ungrouping them, then selecting all the shapes and pressing the exclusion(/intersection/?) works.

What does it mean when I select 2 objects, pick DIFFERENCE… and it does nothing? (It’s just simple text over an image.)
I assume I have 2 “wrong” types of objects selected.
How do I convert between:
Text Image Object Path Other “Things”.How many types of “things” are there?

hi Sally, I hope u come back and check out this post, I know its been a couple months BUT ANYWAY you have to hit “select all” its on the view or edit tab, took me foreevr to figure it out

Jev – don’t group the first items, “combine” them
Carol – same thing. Select the first two boxes and “combine” them, then you can use the third to “divide” themLots of operations don’t work on “groups” of objects, but if you “combine” them into one path, the operations work as described

I’m trying to intersect a circle with a picture, so the picture fits inside the circle (like a view port), but I can’t get the function to work. It works when I do the same thing with a square, but not the picture.
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