This volume covers substantially the central areas of a one-semester course in automata theory. It is oriented towards a mathematical perspective that is understandable to non-mathematicians. Comprehension is greatly aided by examples. Special attention is given to semi-automata theory - the relationship between semigroups and sequential machines (including Greens relations), Schutzenbergers maximal subgroup, von Neumann inverses, wreath products, transducers using matrix notation, shuffle and Kronecker shuffle products. Methods of formal power series, the ambiguity index and linear languages are discussed. Core material includes finite state automata, regular expressions, Kleenes theorem, Chomskys hierarchy and transformations of grammars. Ambiguous grammars (not linited to context-free grammars) and modal logics are briefly discussed. Turing machine variants with many examples, pushdown automata and their state transition diagrams and parsers, linear bounded automata/2-PDA and Kuroda normal form are also discussed. A brief study of Lindenmeyer systems is offered as a comparison to the theory of Chomsky.