Cover art, contributed by **
N. Elkies**

**Henri Darmon, David Ellwood, Brendan
Hassett and Yuri Tschinkel**, Editors' introduction,
pdf

**N. Elkies**,
On the cover: Rational curves on a K3 surface,
pdf

**H. Darmon**,
Rational points on curves,
pdf

**H. Chapdelaine**,
Non-abelian descent and the generalized Fermat equation,
pdf

**M. Rebolledo**,
Merel's theorem on the boundedness of the torsion of elliptic curves,
pdf

**P. Charollois**,
Generalized Fermat equations (d'après Halberstadt-Kraus),
pdf

**S. Dasgupta and J. Voight**,
Heegner points and Sylvester's conjecture,
pdf

**J. Voight**,
Shimura curve computations,
pdf

**M. Greenberg**,
Computing Heegner points arising from Shimura curve parametrizations,
pdf

**M. Greenberg**,
The arithmetic of elliptic curves over imaginary quadratic fields and Stark-Heegner points,
pdf

**Yu. I. Manin**,
Lectures on modular symbols,
pdf

**B. Hassett**,
Rational surfaces over nonclosed fields,
pdf

**D. Harari**,
Non-abelian descent,
pdf

** B. G. Vioreanu**,
Mordell-Weil Problem for Cubic Surfaces, Numerical Evidence,
pdf

**Y. Tschinkel**, Algebraic varieties with many rational points,
pdf

**D. Abramovich**,
Birational geometry for number theorists,
pdf

**J. Starr**,
Arithmetic over function fields,
pdf

**N. Ratazzi, E. Ullmo**,
Galois+Equidistribution = Manin-Mumford,
pdf

**E. Ullmo, A. Yafaev**,
The Andre-Oort conjecture for products of modular curves,
pdf

**C.-L. Chai, F. Oort**,
Moduli of abelian varieties and *p*-divisible groups,
pdf

**D. Kaledin**,
Cartier isomorphism and Hodge Theory in the non-commutative case,
pdf