Finite dimensional rank 2 Nichols algebras of diagonal type I: Examples
  Nichols algebras naturally appear in the classification of finite dimensional pointed Hopf algebras. Assuming only that the base field has characteristic zero several new finite dimensional rank 2 Nichols algebras of diagonal type are listed. Each of them is described in terms of generators and relations. A Poincar\'e--Birkhoff--Witt basis of all of these Nichols algebras is given and their dimension is computed. Together with the continuation of this paper this gives an answer to a question of Andruskiewitsch.   Key Words: Hopf algebra, Lyndon words, full binary tree 
I. Heckenberger