Peaks andThe main subject of this thesis is diagram rewriting.This is a generalisation to dimension~$2$ of word rewriting (in dimension~$1$). In a first time, we give the first convergent diagrammatic presentation of the PRO of linear maps in arbitrary field. Then we study the convergent diagrammatic presentation of matrix of isometries of $RR^n$. We focus especially on a rule similar to the Yang-Baxter equation, described by a certain map $h$. We use the confluence of critical the parametric diagrams, To study the algebraic properties of $h$, Finally, we present the $Sigma$-diagrams, an alternative approach for calculation in bialgebras. We illustrate this approach with examples. The last two chapters have been already published: Diagram rewriting for orthogonal matrices: a study of critical peaks, avec Yves Lafont, Lecture Notes in Computer Science 5117, p. 232-245, 2008 Properties of co-operations: diagrammatic proofs, Mathematical Structures in Computer Science 22(6), p. 970-986, 2012. / The main subject of this thesis is diagram rewriting.This is a generalisation to dimension~$2$ of word rewriting (in dimension~$1$). In a first time, we give the first convergent diagrammatic presentation of the PRO of linear maps in arbitrary field. Then we study the convergent diagrammatic presentation of matrix of isometries of $RR^n$. We focus especially on a rule similar to the Yang-Baxter equation, described by a certain map $h$. We use the confluence of criticalthe parametric diagrams, To study the algebraic properties of $h$, Finally, we present the $Sigma$-diagrams, an alternative approach for calculation in bialgebras. We illustrate this approach with examples. The last two chapters have been already published: Diagram rewriting for orthogonal matrices: a study of critical peaks, avec Yves Lafont, Lecture Notes in Computer Science 5117, p. 232-245, 2008 Properties of co-operations: diagrammatic proofs, Mathematical Structures in Computer Science 22(6), p. 970-986, 2012.