What type of oil does a troy built tiller use? I have lost my book.

This is dependent upon what the engine application on the tiller is. If it's 2-stroke, use a quality synthetic or semi-synthetic 2-stroke oil mixed with the gas. If it has a 4 stroke engine use SAE30 oil, unless you run synthetic (which I highly recommend), then you can use a multi-viscosity oil if you like, say 10W-30.