Please be noted that all capacities listed here are approximate. Check fluid levels when adding or refilling as recommended in your 2001 BMW Z3 user's manual. Keep in mind that all information here is provided “as is” without any warranty of any kind.
Before doing any DIY service please check your insurance policy and BMW warranty policy for your region. In some regions DIY service may invalidate your warranty.
DIY car service is not as difficult as it looks like and it might save you thousands of dollars per year. It might be even fun and a good thing to do with your kids on a weekend to teach them how basic machinery works. It's really hard to screw something up and damage your car permanently if you use right tools, follow BMW Z3 service manual and use right parts and fluids in prescribed amounts. Even modern cars stuffed with electronics can be serviced in your garage or even in your driveway. Changing engine oil, brake fluid, ATF, replacing brake pads, and etc. It's all may be done by yourself in a mater of a couple of hours.
Doing basic service for your 2001 BMW Z3 you're not only saving money, but also also improving your technical skills and learning something new.