The aim of this talk is to give a brief introduction to convex bodies: polytopes, polyhedra, and cones. Starting with the most elementary definitions, and motivated in part by constructions from toric geometry, I hope to address:

• The dual definitions of a polytope, and how this naturally gives rise to polyhedra;
• The concept of finite part and tail cone;
• The basic combinatorial properties of polytopes;
• Computing the basis of a cone;
• Lattice point counting.