The Search for Extra-terrestrial Intelligence (SETI) has for sixty years attempted to solve Fermi's paradox: if intelligent life is relatively common in the universe, where is everybody? Examining SETI through this lens, this volume summarises current thinking on the prevalence of intelligent life in the universe, and discusses sixty-six distinct solutions to the so-called paradox. It describes the methodology of SETI, and how many disciplines feed into the debate, from physics and biology, to philosophy and anthropology. The presented solutions are organised into three key groups: rare-Earth solutions, suggesting planetary habitability, life and intelligence are uncommon; catastrophist solutions, arguing civilisations do not survive long enough to make contact; and non-empirical solutions, those that take theoretical approaches, such as that our methodology is flawed. This comprehensive introduction to SETI concludes by looking at the future of the field and speculating on humanity's potential fate.