We will show how we glue two monomial curves $A$ and $B$ to get a monomial curve $C$.  This notion of gluing due to Delorme and Rosales arose from a generalization of the well known structure theorems for space monomial curves. Then we use mapping cylinders to build the resolution of $C$ from those of $A$ and $B$.   This explicit construction then yields many formulae for the invariants of $C$ in terms of the invariants of $A$ and $B$.

This is joint work with Philippe Gimenez.