This chapter starts by discussing the Robinson-Schensted correspondence that maps permutations to a pair of Standard Young Tableaux of the same shape, and some of its many consequences. Applications to counting pattern avoiding permutations and involutions are presented. We also survey some partially ordered sets of permutations, such as the Bruhat order, the Weak Bruhat order, and the pattern containment order. We close the chapter by studying some simplicial complexes of permutations, and permutation classes. In the exercises, a new family of questions related to pattern avoiding permutations with a unique longest increasing subsequence is addressed.