I purchased a transformer like the one shown here:

http://sound.westhost.com/xfmr-2a.jpg

I believe it uses an E-I Lamination set.

Unfortuanately it's not incased in anything and the transformer is completely exposed. Now that being said, are there any dangers to having an exposed core? I know you'll get a nice shock if you touch the wires, but do I also have to take precautions to cover the core up? If I'm not mistaking touching the core will not give you a shock.

By the way this is for a school project, so the average person will not be exposed to it. I just don't want to lose marks for safety.

 

That is correct. The core laminations carry no voltage. It is safe as long as the voltage terminals are covered, but placing it in an enclosed box is best.

 

Adding to what Beenthere suggests, if the enclosure is metallic, said enclosure should be connected to earth ground. If the enclosure is non-metal or an insulator, you should connect earth ground to one of the transformer's mounting flanges.

Please use a suitably rated fuse in the incoming "hot" or "line" wire; normally black in color. The fuse should be before any other component; even the power switch.

For insulation of the soldered connections, use suitably sized heat shrink tubing. Do not use "electrical tape" or "electrician's tape" as insulation, as it is not permanent.