Asbestos Safety Training
Radiation Safety Training
Most of you will end up needing to work with radioactive materials in the course of your thesis work. To become qualified to do so, you will have to undertake formal radiation safety training, and it is best to do that in your first year. Otherwise, you might well end up not being allowed to perform key experiments in your thesis research. Training is offered by Environmental Health; you should check their website for a schedule of courses offered.
On the other hand, if your thesis is very unlikely to include any experimental work (such as if it is to be entirely computational), then you might not need this training and do not have to take it now.
Additional Safety Training
The University of Washington takes safety training seriously and offers a large number of safety courses via Environmental Health.