What are vector graphics?
Vector graphics are defined by mathematical relationships and by points, lines, and shapes. They are not defined by pixels, the way a photographic image is. A circle created in vector software would be defined by a number of points, by an x/y position, and by other information, such as color, width of the stroke. In the Adobe Creative Cloud, Illustrator is the vector program. There are many other vector programs, Inkscape is an open-source application. In this class, we will be using Illustrator.
Vector files are used widely in digital fabrication. We will be using vector files to cut with the vinyl cutters and with the laser cutter. Generally it is important that the paths you create in Illustrator are closed paths, though there are exceptions.
Depending on what type of digital fabrication machine you are using, you may need to prepare your files differently. Stroke width and sometimes stroke color are important in files to be cut on a laser cutter, this does not matter for files to be cut with the vinyl cutter, but the file format that you load may be important.
While there are many other ways to make paths with Adobe Illustrator or other vector software, mastering the pen tool is extremely helpful. Students who take this course should have some experience with Illustrator, this is a quick review.
Drawing with the Pen Tool in Illustrator
In a vector drawing program, lines and shapes are defined as paths made up of anchor points. An open path is a line, a closed path is a shape. There are 2 kinds of anchor points, corner points and smooth points. Corner points define straight lines, smooth points define curves. The smooth points have handles coming out of them that determine the arc of the curve.
If you want to make an open path, click to set down corner points, click and drag to set down smooth points, adjusting the length of the handles to control the arc of the curve. When you have completed the line, hit the Return or Enter key.
To make a closed path, set down your anchor points. When you are ready to close the path, click on the first anchor point. The pen tool cursor will have a little circle next to it, indicating that it will close the path.
Combining Shapes with Pathfinder
There are a number of shape tools available in Illustrator, including rectangle, ellipse, You can combine these shapes to make more complex paths using the Pathfinder panel (Window Menu>Pathfinder).
Draw the shapes on the Artboard, with them overlapping in the manner you want to combine them. To combine the shapes into one form, click on the first icon under Shape Modes. The result will look like this.
If you want to subtract one shape from another, you can use the Subtract Front icon, the second one under Shape Modes.
Combining Shapes with the Shape Builder Tool
You can also combine shapes with the Shape Builder Tool. This tool is in the tool palette. 
Draw 2 shapes on the Artboard. Make sure they are both select4ed. Select the Shape builder tool.
When you roll over the shapes, they will have a fine grid of many gray dots over them Click and drag over them with the tool, and the shapes will be merged.
