After working on research topics related to seismic tomography for a quarter of a century, I decided it was time to write down all I know about the topic – but not in a grand unifying tome that covers everything from first principles to numerical applications. First of all, I have little patience for mathematical niceties; second, and more importantly, I wrote this book for the practitioners of the craft of seismic tomography. Those who go out into the field to collect data usually have no time for proofs of convergence or existence. The intended reader of this book is therefore an observational seismologist or helioseismologist who is not interested in lengthy derivations nor in the subtleties that fascinate the theoreticians, but who wants to understand the assumptions behind algorithms, even if these are mathematically intricate, and develop an understanding of the conditions for their validity, which forms the basis of that priceless commodity: scientific intuition. The level is such that it could be used for a one-semester course at upper undergraduate or beginning graduate level, perhaps following up on an introductory course based on Shearer or Stein and Wysession. Despite covering a wide range of topics, I have tried to keep it short (hence the title), while not economizing on references that may provide more detail if needed.