We present far-UV spectroscopy obtained with HST for 48 blue objects in the core of 47 Tuc. Based on their position in a FUV-optical colour-magnitude diagram, these were expected to include cataclysmic variables (CVs), blue stragglers (BSs), white dwarfs (WDs) and other exotic objects. For a subset of these sources, we also construct FUV-NIR SEDs. Based on our analysis of this extensive data set, we report the following main results. (1) We spectroscopically confirm 3 previously known or suspected CVs via the detection of emission lines and find new evidence for dwarf nova eruptions in two of these. (2) Only one other source in our spectroscopic sample exhibits marginal evidence for line emission, but predicted and observed CV numbers still agree to within a factor of about 2-3. (3) We have discovered a hot (T_eff = 8700 K), low-mass (M = 0.05 M_sun) secondary star in a previously known 0.8 day binary system. This exotic object is probably the remnant of a subgiant that has been stripped of its envelope and may represent the ``smoking gun of a recent dynamical encounter. (4) We have found a Helium WD, the second to be optically detected in 47 Tuc, and the first outside a millisecond-pulsar system. (5) We have discovered a BS-WD binary system, the first known in any globular cluster. (6) We have found two additional candidate WD binary systems with putative main sequence and subgiant companions. (7) We estimate the WD binary fraction in the core of 47 Tuc to be 15 +17/-9 (stat) +8/-7 (sys). (8) One BS in our sample may exceed twice the cluster turn-off mass, but the uncertainties are large. Taken as a whole, our study illustrates the wide range of stellar exotica that are lurking in the cores of GCs, most of which are likely to have undergone significant dynamical encounters. [abridged]
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