  These lecture notes were prepared for a 25-hour course for advanced
undergraduate students participating in Perimeter Institute's Undergraduate
Summer Program. The lectures cover some of what is currently known about the
possibility of superluminal travel and time travel within the context of
established science, that is, general relativity and quantum field theory.
Previous knowledge of general relativity at the level of a standard
undergraduate-level introductory course is recommended, but all the relevant
material is included for completion and reference. No previous knowledge of
quantum field theory, or anything else beyond the standard undergraduate
curriculum, is required. Advanced topics in relativity, such as causal
structures, the Raychaudhuri equation, and the energy conditions are presented
in detail. Once the required background is covered, concepts related to
faster-than-light travel and time travel are discussed. After introducing
tachyons in special relativity as a warm-up, exotic spacetime geometries in
general relativity such as warp drives and wormholes are discussed and
analyzed, including their limitations. Time travel paradoxes are also discussed
in detail, including some of their proposed resolutions.
