Where can I find a book which explains the development of modern logic, e.g. Tarski, Frege, Peano, up untill Wittgenstein, Russel?



History of Logic Development
The scope of the figures you mention (Tarski, Frege, Peano, Wittgenstein, Russell) makes it a little unclear exactly what you're after. For instance, *From Frege to Goedel* (as mentioned by Mahmud) is an excellent compilation of early texts in mathematical logic -- you get e.g. Frege, Peano, Hilbert, Zermelo, Skolem, Herbrand, Goedel -- with helpful introductions included, but the focus is on the primary texts, rather than giving a single, unified account of the development of logic. And its relative lack of a philosophical focus means there's nothing like Russell or Wittgenstein to be found. [N.B. Along similar lines to this work, the two volumes of *From Kant to Hilbert* offer a more wide-ranging (in terms of subject and chronology) cross-section of works in the foundations of mathematics; note, though, that mathematical logic per se is *not* the focus there.]


Not knowing your background, or your exact goal, I would tentatively recommend Benacerraf and Putnam's *Philosophy of Mathematics: Selected Readings*. It has a great selection of works by the likes of Frege, Russell, Hilbert, Brouwer, Goedel, Von Neumann, Quine, and so on (and Wittgenstein is mentioned aplenty). In total, you get a lot about the interplay between technical matters in mathematical logic, foundations of math, and also related issues of a more straight-up philosophical nature (if you're into that sort of thing). It too doesn't give a single chronological narrative, but just skipping around the articles in that collection will give you a lot to chew on, and ultimately give you a better account of the development of modern logic than will primary sources (IMHO).


