The first of a two volume set showcasing current research in model theory and its connections with number theory, algebraic geometry, real analytic geometry and differential algebra. Contents - 1. Model theory and stability theory, with applications in differential algebra and algebraic geometry Anand Pillay; 2. Differential algebra and generalizations of Grothendieck’s conjecture on the arithmetic of linear differential equations Anand Pillay; 3. Schanuel’s conjecture for non-isoconstant elliptic curves over function fields Daniel Bertrand; 4. An afterthought on the generalized Mordell-Lang conjecture Damian Rössler; and more.