We measure the mass of b-hadrons in exclusive J/-decay modes. The correct momentum scale is established by the following steps: validate and quantify distortions or systematic effects in the Central Outer Tracker and Silicon Vertex Detector, apply and fine tune the energy loss corrections per track, and finally tune the magnetic field scale. With the momentum scale established, we find: m(B +) = 5279.10 ± 0.41 (stat) 0.36 (sys), m(B°) = 5279.63 ± 0.53 (stat) 0.33 (sys), m(B°) = 5366.01 ± 0.73 (stat) 0.33 (ys), m(Ab) = 5619.7 ± 1.2 (stat) 1.2 (sys) MeV/c 2. Ista Horribilis Taetraque Finita est Passio anonymous The acknowledgment section of every thesis is in a way also an account of that phase in one's life. But compressing the last years into a few pages is of course an impossible task. I would like to thank my advisor Prof. Christoph Paus for giving me the opportunity to come to MIT. I admire him as the hardest working person I know. I would like to thank him and my academic advisor Bolek Wyslouch for their guidance through the rough waters at the institute. I'm indebted to my previous science educators, in particular Prof. Hebbeker, Prof. Keiper and my high school teacher Mr. Mahn. I would like to thank the MIT group for sharing the burden of grad school experience with me. My fellow graduate students Ivan Furic, Konstantin Anikeev, Mike Mulhearn and Sasha Rakitine provided the atmosphere needed, to get the work done. Thanks to the younger students, Alberto Belloni, Arkady Bolshov, Boris Iyutin, Nuno Leonardo and Jeff Miles for freeing my time during the last year, by taking over our hardware responsibilities. David Starr contributed to this work with his undergraduate thesis. Gerry Bauer's broad scientific curiosity was a constant inspiration. From Steve Tether I learned a lot about computing and more Science-Fiction anecdotes than I can remember. I gained more than one insight during discussions with Sham Sumorok. And if you would have paid attention, you too would have noticed his dry British humor as a welcome entertainment at group meetings. Jeff Tseng always had an open door and we talked about physics and beyond. Ilya Kravchenko is not only a good collegue, I consider him a friend. Getting to know the previous generation of the CDF MIT group Prof.