Thebook provides thefirst full length exploration of fuzzy computability. It describes the notion of fuzziness and present the foundation of computability theory.It thenpresents the various approaches to fuzzy computability. This text provides a glimpse into the different approaches in this area, whichis important for researchers in order to have a clear view of the field. Itcontains a detailed literature review and the author includesall proofs to make the presentation accessible. Ideas for future research and explorations are also provided. Students and researchers in computer science and mathematics will benefit from this work.