Mathematical Preliminaries.- Cardinalities and Diagonalization.- Binary Relations.- Mathematical Logic, Induction, Proofs.- Dealing with Recursion.- Strings and Languages.- Machines, Languages, DFA.- NFA and Regular Expressions.- Operations on Regular Machinery.- The Automaton/Logic Connection, Symbolic Techniques.- The 'Pumping' Lemma.- Context-free Languages.- Push-down Automata and Context-free Grammars.- Turing Machines.- Basic Undecidability Proofs.- Advanced Undecidability Proofs.- Basic Notions in Logic including SAT.- Complexity Theory and NP-Completeness.- DFA for Presburger Arithmetic.- Model Checking: Basics.- Model Checking: Temporal Logics.- Model Checking: Algorithms.- Conclusions.