In recent years, speech recognition devices have become central to our everyday lives. Systems such as Siri, Alexa, speech-to-text, and automated telephone services, are built by people applying expertise in sound structure and natural language processing to generate computer programmes that can recognise and understand speech. This exciting new advancement has led to a rapid growth in speech technology courses being added to linguistics programmes; however, there has so far been a lack of material serving the needs of students who have limited or no background in computer science or mathematics. This textbook addresses that need, by providing an accessible introduction to the fundamentals of computer speech synthesis and automatic speech recognition technology, covering both neural and non-neural approaches. It explains the basic concepts in non-technical language, providing step-by-step explanations of each formula, practical activities and ready-made code for students to use, which is also available on an accompanying website.