## Introduction

The central topic of the school is the mutual interaction of algebra, combinatorics and geometry. Objects of research in algebraic geometry are affine as well as projective varieties and their associated invariants which can be studied using methods from algebra and combinatorics. Toric and tropical varieties are instances where such kind of approaches were and still are very successful. In discrete geometry cones, graphs, hyperplane arrangements and matroids are examples of research subjects which naturally play prominent roles in algebra and discrete mathematics. The main goal of this school is to build bridges between various disciplines of mathematics which have in common to apply algebraic and combinatorial methods in geometry. The lectures range from the foundations to recent results and applications of the relevant theory.