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These notes were given as lectures at the CERN Winter School on Supergravity,Strings and Gauge Theory 2010. We describe the structure of scatteringamplitudes in gauge theories, focussing on the maximally supersymmetric theoryto highlight the hidden symmetries which appear. Using the BCFW recursionrelations we solve for the tree-level S-matrix in N=4 super Yang-Mills theory,and describe how it produces a sum of invariants of a large symmetry algebra.We review amplitudes in the planar theory beyond tree-level, describing theconnection between amplitudes and Wilson loops, and discuss the implications ofthe hidden symmetries.

Hidden Simplicity of Gauge Theory Amplitudes