Let's start on Intermediate Techniques.

Create a Rectangle and Oval shape.

Move them so they overlap.

Click on Path -> Union or 'CTRL' + '+'.

When you Union them, they become a single shape.

Instead if you chose Path -> Difference or 'CTRL' + '-'.

The shape on Top will be cut out of the shape on Bottom.

If you choose Path -> Intersection or 'CTRL' + '*'.

Only the Overlapping shape will persist.

Clicking on Path -> Exclusion.

Will only remove the section where there was an Overlap.

Clicking on Path -> Division or 'CTRL' + '/'.

Will cut out, but keep, the overlapped section.

Lastly if you select the Path -> Cut Path or 'CTRL' + 'ALT' + '/'.

Only the Path will stay. In addition it will cut and keep the overlapped path.

To demonstrate Dynamic Offset, create an Oval shape.

Then Duplicate it ('CTRL' + 'D').

Click on Path -> Dynamic Offset or 'CTRL' + 'J'.

Then find the Diamond shape.

Left-Click and drag this to start offsetting the Duplicated oval.

Then Release your mouse to finish.

Moving around a Dynamic Offset shape can slow down Inkscape.

Make sure to set it back to a Path when you're finished.

Let's talk about Grouping shapes.

If you Select your 2 previous shapes.

You can then click on Object -> Group or 'CTRL' + 'G'.

The Shapes will now stay together.

You can always use Object -> Ungroup or 'SHIFT' + 'CTRL' + 'G'.

And the shapes will Separate.

To try out Simplify, start by using the Calligraphy Tool to make a shape.

With the new shape Selected, use the Node Tool and you'll see a lot of nodes.

If you clicked on Path -> Simplify or 'CTRL' + 'L'.

The shape will be Simplified by reducing the amount of nodes, but maintaining the shape (somewhat).

You can Simplify it as much as you want, but it will start losing it's shape the more you do it.

(This tutorial may continue to be updated!)