This volume contains the lecture notes from the courses o?ered at the Inter- tional Summer School on Language Engineering and Rigorous Software De- lopment, held in Piriap ' olis, Uruguay, from February 25 to March 1, 2008. The aim of the schoolwasthe dissemination of advancedscienti?c knowledge in the areas of programming languages and rigorous methods for software - velopment. The school was oriented to computer science graduate students and researchers,withaninterestinformaltechniquesforthedesignandconstruction of software systems as well as programming languages. The school was organized in the context of the LERnet (Language En- neering and Rigorous Software Development) project. LERnet is a project of the ALFA programme of the European Commission for co-operation between higher education institutions of the European Union and Latin America. The institutions that participate in the LERnet project are the following: - Chalmers Tekniska H.. ogskola, Sweden - Institut National de la Recherche en Informatique et Automatique (INRIA), France - Universidad de Castilla-La Mancha, Spain - Universidad Catol ' ica de Santiago del Estero, Argentina - Universidad EAFIT, Colombia - Universidade Federal de Minas Gerais, Brazil - Universidade do Minho, Portugal - Universidad Nacional de San Luis, Argentina - Universidad Polit' ecnica de Valencia, Spain - Universidad de la Republica ' , Uruguay - Universiteit Utrecht, The Netherlands The project oversees the mobility of PhD students from Latin America to the European Union and vice versa for a period of up to 18 months, to pursue

The use of mathematical methods in the development of software is essential when reliable systems are sought; in particular they are now strongly recommended by the official norms adopted in the production of critical software. Program Verification is the area of computer science that studies mathematical methods for checking that a program conforms to its specification. This text is a self-contained introduction to program verification using logic-based methods, presented in the broader context of formal methods for software engineering. The idea of specifying the behaviour of individual software components by attaching contracts to them is now a widely followed approach in program development, which has given rise notably to the development of a number of behavioural interface specification languages and program verification tools. A foundation for the static verification of programs based on contract-annotated routines is laid out in the book. These can be independently verified, which provides a modular approach to the verification of software. The text assumes only basic knowledge of standard mathematical concepts that should be familiar to any computer science student. It includes a self-contained introduction to propositional logic and first-order reasoning with theories, followed by a study of program verification that combines theoretical and practical aspects - from a program logic (a variant of Hoare logic for programs containing user-provided annotations) to the use of a realistic tool for the verification of C programs (annotated using the ACSL specification language), through the generation of verification conditions and the static verification of runtime errors.