A Concise Introduction to Mathematical Logic : Springer : 9781441912206 : 1441912207 : 17 Dec 2009 : by Lev Beklemishev, Moscow The ?eld of mathematical logic?evolving around the notions of logical validity, provability, and computation?was created in the ?rst half of the previous century by a cohort of brilliant mathematicians and philosophers such as Frege, Hilbert, Gödel, Turing, Tarski, Malcev, Gentzen, and some others. The development of this discipline is arguably among the highest achievements of science in the twentieth century: it expanded mat- matics into a novel area of applications, subjected logical reasoning and computability to rigorous analysis, and eventually led to the creation of computers. The textbook by Professor Wolfgang Rautenberg is a well-written - troduction to this beautiful and coherent subject. It contains classical material such as logical calculi, beginnings of model theory, and Gödel's incompleteness theorems, as well as some topics motivated by appli-